What is the derivative of ${tan}^{4} (x)$ $tan^4 (x)$ ?

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Answer 1 · 2016-01-22T03:23:03

$\frac{d}{d x} [{tan}^{4} (x)] = 4 {tan}^{3} (x) {sec}^{2} (x)$ $d/dx[tan^4(x)]=4tan^3(x)sec^2(x)$

The overriding issue is the fourth power. You can deal with it through the chain rule:

$d/dx[u^4]=4u^3*u'$

Here, we have $u=tan(x)$ , so

$d/dx[tan^4(x)]=4tan^3(x)*d/dx[tan(x)]$

Know that $d/dx[tan(x)]=sec^2(x)$ , hence

$d/dx[tan^4(x)]=4tan^3(x)sec^2(x)$

What is the derivative of tan^4 (x)tan4(x)tan^4 (x)?