Calculus Examples

$y = \arctan (x)$

Step 1

Differentiate both sides of the equation.

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

Step 2

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

$y'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

The derivative of $\arctan (x)$ with respect to $x$ is $\frac{1}{1 + x^{2}}$ .

$\frac{1}{1 + x^{2}}$

Step 3.2

Reorder terms.

$\frac{1}{x^{2} + 1}$

Step 4

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

$y' = \frac{1}{x^{2} + 1}$

Step 5

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

$\frac{d y}{d x} = \frac{1}{x^{2} + 1}$