Calculus Examples

$y = X^{8}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d X} (y) = \frac{d}{d X} (X^{8})$

Step 2

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

$y'$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d X} [X^{n}]$ is $n X^{n - 1}$ where $n = 8$ .

$8 X^{7}$

Step 4

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

$y' = 8 X^{7}$

Step 5

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

$\frac{d y}{d X} = 8 X^{7}$