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Question

Let f(x)=sinx,g(x)=x2,h(x)=logex. If F(x)=(hogof)(x), then F''(x) is equal to


A

acosec3x

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B

2cotx2-4x2cosec2x2

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C

2cotx2

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D

-2cosec2x

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Solution

The correct option is D

-2cosec2x


Explanation for the correct option.

Find the value of F''(x):

Given,

f(x)=sinx,g(x)=x2,h(x)=logex and

F(x)=h(g(f(x)))=h(g(sinx))=h(sin2x)=logesin2x

Now differentiate F(x) w. r. t. x.

F'(x)=1sin2x2sinxcosx=2cotx

Again differentiate F'(x) w.r.t. x.

F''(x)=-2cosec2x[∵ddx(cotx)=-cosec2x]

Hence the correct option is D.


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