Calculus Examples

$\frac{d^{36}}{d x^{36}} (- 7 \sin (x))$

Step 1

Find the first derivative.

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Step 1.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 1.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f' (x) = - 7 \cos (x)$

Step 2

Find the second derivative.

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Step 2.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 2.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 2.3

Multiply $- 1$ by $- 7$ .

$f'' (x) = 7 \sin (x)$

Step 3

Find the third derivative.

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Step 3.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 3.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f''' (x) = 7 \cos (x)$

Step 4

Find the fourth derivative.

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Step 4.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 4.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 4.3

Multiply $- 1$ by $7$ .

$f^{4} (x) = - 7 \sin (x)$

Step 5

Find the 5th derivative.

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Step 5.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 5.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{5} (x) = - 7 \cos (x)$

Step 6

Find the 6th derivative.

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Step 6.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 6.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 6.3

Multiply $- 1$ by $- 7$ .

$f^{6} (x) = 7 \sin (x)$

Step 7

Find the 7th derivative.

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Step 7.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 7.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{7} (x) = 7 \cos (x)$

Step 8

Find the 8th derivative.

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Step 8.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 8.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 8.3

Multiply $- 1$ by $7$ .

$f^{8} (x) = - 7 \sin (x)$

Step 9

Find the 9th derivative.

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Step 9.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 9.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{9} (x) = - 7 \cos (x)$

Step 10

Find the 10th derivative.

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Step 10.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 10.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 10.3

Multiply $- 1$ by $- 7$ .

$f^{10} (x) = 7 \sin (x)$

Step 11

Find the 11th derivative.

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Step 11.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 11.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{11} (x) = 7 \cos (x)$

Step 12

Find the 12th derivative.

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Step 12.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 12.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 12.3

Multiply $- 1$ by $7$ .

$f^{12} (x) = - 7 \sin (x)$

Step 13

Find the 13th derivative.

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Step 13.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 13.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{13} (x) = - 7 \cos (x)$

Step 14

Find the 14th derivative.

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Step 14.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 14.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 14.3

Multiply $- 1$ by $- 7$ .

$f^{14} (x) = 7 \sin (x)$

Step 15

Find the 15th derivative.

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Step 15.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 15.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{15} (x) = 7 \cos (x)$

Step 16

Find the 16th derivative.

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Step 16.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 16.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 16.3

Multiply $- 1$ by $7$ .

$f^{16} (x) = - 7 \sin (x)$

Step 17

Find the 17th derivative.

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Step 17.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 17.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{17} (x) = - 7 \cos (x)$

Step 18

Find the 18th derivative.

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Step 18.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 18.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 18.3

Multiply $- 1$ by $- 7$ .

$f^{18} (x) = 7 \sin (x)$

Step 19

Find the 19th derivative.

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Step 19.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 19.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{19} (x) = 7 \cos (x)$

Step 20

Find the 20th derivative.

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Step 20.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 20.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 20.3

Multiply $- 1$ by $7$ .

$f^{20} (x) = - 7 \sin (x)$

Step 21

Find the 21st derivative.

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Step 21.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 21.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{21} (x) = - 7 \cos (x)$

Step 22

Find the 22nd derivative.

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Step 22.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 22.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 22.3

Multiply $- 1$ by $- 7$ .

$f^{22} (x) = 7 \sin (x)$

Step 23

Find the 23rd derivative.

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Step 23.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 23.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{23} (x) = 7 \cos (x)$

Step 24

Find the 24th derivative.

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Step 24.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 24.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 24.3

Multiply $- 1$ by $7$ .

$f^{24} (x) = - 7 \sin (x)$

Step 25

Find the 25th derivative.

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Step 25.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 25.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{25} (x) = - 7 \cos (x)$

Step 26

Find the 26th derivative.

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Step 26.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 26.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 26.3

Multiply $- 1$ by $- 7$ .

$f^{26} (x) = 7 \sin (x)$

Step 27

Find the 27th derivative.

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Step 27.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 27.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{27} (x) = 7 \cos (x)$

Step 28

Find the 28th derivative.

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Step 28.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 28.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 28.3

Multiply $- 1$ by $7$ .

$f^{28} (x) = - 7 \sin (x)$

Step 29

Find the 29th derivative.

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Step 29.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 29.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{29} (x) = - 7 \cos (x)$

Step 30

Find the 30th derivative.

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Step 30.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 30.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 30.3

Multiply $- 1$ by $- 7$ .

$f^{30} (x) = 7 \sin (x)$

Step 31

Find the 31st derivative.

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Step 31.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 31.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{31} (x) = 7 \cos (x)$

Step 32

Find the 32nd derivative.

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Step 32.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 32.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 32.3

Multiply $- 1$ by $7$ .

$f^{32} (x) = - 7 \sin (x)$

Step 33

Find the 33rd derivative.

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Step 33.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \sin (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\sin (x)]$ .

$- 7 \frac{d}{d x} [\sin (x)]$

Step 33.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{33} (x) = - 7 \cos (x)$

Step 34

Find the 34th derivative.

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Step 34.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 \cos (x)$ with respect to $x$ is $- 7 \frac{d}{d x} [\cos (x)]$ .

$- 7 \frac{d}{d x} [\cos (x)]$

Step 34.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- 7 (- \sin (x))$

Step 34.3

Multiply $- 1$ by $- 7$ .

$f^{34} (x) = 7 \sin (x)$

Step 35

Find the 35th derivative.

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Step 35.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)]$

Step 35.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$f^{35} (x) = 7 \cos (x)$

Step 36

Find the 36th derivative.

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Step 36.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \cos (x)$ with respect to $x$ is $7 \frac{d}{d x} [\cos (x)]$ .

$7 \frac{d}{d x} [\cos (x)]$

Step 36.2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$7 (- \sin (x))$

Step 36.3

Multiply $- 1$ by $7$ .

$f^{36} (x) = - 7 \sin (x)$