Calculus Examples

$10 x + 3 y = 4 \sin (y)$

Step 1

Find the first derivative.

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Step 1.1

Since $4$ is constant with respect to $y$ , the derivative of $4 \sin (y)$ with respect to $y$ is $4 \frac{d}{d y} [\sin (y)]$ .

$4 \frac{d}{d y} [\sin (y)]$

Step 1.2

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

$f' (y) = 4 \cos (y)$

Step 2

Find the second derivative.

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Step 2.1

Since $4$ is constant with respect to $y$ , the derivative of $4 \cos (y)$ with respect to $y$ is $4 \frac{d}{d y} [\cos (y)]$ .

$4 \frac{d}{d y} [\cos (y)]$

Step 2.2

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

$4 (- \sin (y))$

Step 2.3

Multiply $- 1$ by $4$ .

$f'' (y) = - 4 \sin (y)$