Calculus Examples

$y = \cos (X)$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d X} (y) = \frac{d}{d X} (\cos (X))$

Step 2

The derivative of $y$ with respect to $X$ is $y'$ .

$y'$

Step 3

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

$- \sin (X)$

Step 4

Reform the equation by setting the left side equal to the right side.

$y' = - \sin (X)$

Step 5

Replace $y'$ with $\frac{d y}{d X}$ .

$\frac{d y}{d X} = - \sin (X)$