Calculus Examples

$x = y$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (x) = \frac{d}{d x} (y)$

Step 2

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

$1$

Step 3

Rewrite $\frac{d}{d x} [y]$ as $y'$ .

$y'$

Step 4

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

$1 = y'$

Step 5

Rewrite the equation as $y' = 1$ .

$y' = 1$

Step 6

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

$\frac{d y}{d x} = 1$