How do you find the derivative of $tan^4 (x)$ ?

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Answer 1 · 2017-05-19T01:08:43

By using the power rule

$d/(dx)[(u(x))^n] = n [u(x)]^(n-1)$ , where $u(x)$ is a function of $x$ ,

$d/(dx)[f(u)] = (df)/(du)(du)/(dx)$ , where $f = f(u(x))$ .

If we rewrite $tan^4(x)$ as $(tanx)^4$ , we have that:

As a result:

$color(blue)(d/(dx)[f(u)]) = (df)/(du)(du)/(dx)$

$d/(du)[u^4]cdot d/(dx)[tanx]$

$= 4u^3 cdot sec^2x$

$= color(blue)(4tan^3xsec^2x)$

How do you find the derivative of tan^4 (x)tan^4 (x)?