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

Question

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

1 Answer

Impact of this question

8804 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-19T01:08:43

By using the power rule

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

and the chain rule

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

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

$f (u) = u^{4}$ $f(u) = u^4$
$u (x) = tan x$ $u(x) = tanx$

As a result:

$\frac{d}{d x} [f (u)] = \frac{d f}{d u} \frac{d u}{d x}$ $color(blue)(d/(dx)[f(u)]) = (df)/(du)(du)/(dx)$

$\frac{d}{d u} [u^{4}] \cdot \frac{d}{d x} [tan x]$ $d/(du)[u^4]cdot d/(dx)[tanx]$

$= 4 u^{3} \cdot {sec}^{2} x$ $= 4u^3 cdot sec^2x$

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

Science

Math

Humanities

... and beyond

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

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the derivative of tan^4 (x)tan4(x)tan^4 (x)?

1 Answer

Related questions

Impact of this question

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