Calculus Examples

$2 \tan (π x^{5}) \cdot (2 \tan (u))$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Differentiate using the Constant Multiple Rule.

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Step 2.1

Multiply $2$ by $2$ .

$\frac{d}{d u} [4 \tan (π x^{5}) \cdot \tan (u)]$

Step 2.2

Since $4 \tan (π x^{5})$ is constant with respect to $u$ , the derivative of $4 \tan (π x^{5}) \tan (u)$ with respect to $u$ is $4 \tan (π x^{5}) \frac{d}{d u} [\tan (u)]$ .

$4 \tan (π x^{5}) \frac{d}{d u} [\tan (u)]$

Step 3

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

$4 \tan (π x^{5}) \sec^{2} (u)$

Step 4

Reorder the factors of $4 \tan (π x^{5}) \sec^{2} (u)$ .

$4 \sec^{2} (u) \tan (π x^{5})$