Calculus Examples

$f (x) = 8 \sin (π) + 3 \cos (2 π)$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{d}{d x} [8 \sin (0) + 3 \cos (2 π)]$

Step 2

The exact value of $\sin (0)$ is $0$ .

$\frac{d}{d x} [8 \cdot 0 + 3 \cos (2 π)]$

Step 3

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{d}{d x} [8 \cdot 0 + 3 \cos (0)]$

Step 4

The exact value of $\cos (0)$ is $1$ .

$\frac{d}{d x} [8 \cdot 0 + 3 \cdot 1]$

Step 5

By the Sum Rule, the derivative of $8 \cdot 0 + 3 \cdot 1$ with respect to $x$ is $\frac{d}{d x} [8 \cdot 0] + \frac{d}{d x} [3 \cdot 1]$ .

$\frac{d}{d x} [8 \cdot 0] + \frac{d}{d x} [3 \cdot 1]$

Step 6

Evaluate $\frac{d}{d x} [8 \cdot 0]$ .

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Step 6.1

Multiply $8$ by $0$ .

$\frac{d}{d x} [0] + \frac{d}{d x} [3 \cdot 1]$

Step 6.2

Since $0$ is constant with respect to $x$ , the derivative of $0$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [3 \cdot 1]$

Step 7

Evaluate $\frac{d}{d x} [3 \cdot 1]$ .

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Step 7.1

Multiply $3$ by $1$ .

$0 + \frac{d}{d x} [3]$

Step 7.2

Since $3$ is constant with respect to $x$ , the derivative of $3$ with respect to $x$ is $0$ .

$0 + 0$

Step 8

Add $0$ and $0$ .

$0$