How do you differentiate $f (x) = sec 4 x^{5}$ $f(x)=sec4x^5$ ?

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How do you differentiate $f (x) = sec 4 x^{5}$ $f(x)=sec4x^5$ ?

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Answer 1 · 2016-11-02T15:59:18

THe answer is $= 20 x^{4} sec 4 x^{5} tan 4 x^{5}$ $=20x^4sec4x^5tan4x^5$

Explanation:

Firtst, we need rhe derivative of $sec x$ $secx$
We use $(u/v)'=(u'v-uv')/v^2$
$secx =1/cosx$
So $(secx)'=(1/cosx)'=(0*cosx-1*(-sinx))/cos^2x$
$=sinx/cos^2x=secxtanx$
$:.$ $f'(x)=(sec4x^5)'=sec4x^5tan4x^5*(4x^5)'$
$=sec4x^5tan4x^5*20x^4$

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How do you differentiate $f (x) = sec 4 x^{5}$ $f(x)=sec4x^5$ ?

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