Calculus Examples

$y = 2 \tan (x)$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (2 \tan (x))$

Step 2

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

$y'$

Step 3

Differentiate the right side of the equation.

Tap for more steps...

Step 3.1

Since $2$ is constant with respect to $x$ , the derivative of $2 \tan (x)$ with respect to $x$ is $2 \frac{d}{d x} [\tan (x)]$ .

$2 \frac{d}{d x} [\tan (x)]$

Step 3.2

The derivative of $\tan (x)$ with respect to $x$ is $\sec^{2} (x)$ .

$2 \sec^{2} (x)$

Step 4

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

$y' = 2 \sec^{2} (x)$

Step 5

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

$\frac{d y}{d x} = 2 \sec^{2} (x)$