How do you differentiate $f(x)=sec(4x^5)$ ?

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Answer 1 · 2017-08-13T04:08:18

$d/(dx) [sec(4x^5)] = color(blue)(20x^4tan(4x^5)sec(4x^5)$

We're asked to find the derivative

$d/(dx) [sec(4x^5)]$

We can first use the chain rule:

$d/(dx) [sec(4x^5)] = d/(du) [secu] (du)/(dx)$

where

$= tan(4x^5)sec(4x^5)d/(dx) [4x^5]$

We now use the power rule:

$d/(dx)[x^n] = nx^(n-1)$

where $n = 5$ :

$= tan(4x^5)sec(4x^5)5(4x^4)$

$color(blue)(ulbar(|stackrel(" ")(" "20x^4tan(4x^5)sec(4x^5)" ")|)$

How do you differentiate f(x)=sec(4x^5)f(x)=sec(4x^5)?