Calculus Examples

$y = 5 \tan (x)$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (5 \tan (x))$

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

Since $5$ is constant with respect to $x$ , the derivative of $5 \tan (x)$ with respect to $x$ is $5 \frac{d}{d x} [\tan (x)]$ .

$5 \frac{d}{d x} [\tan (x)]$

Step 3.2

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

$5 \sec^{2} (x)$

Step 4

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

$y' = 5 \sec^{2} (x)$

Step 5

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

$\frac{d y}{d x} = 5 \sec^{2} (x)$