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Letf(x)=sinx,g(x)=x^(2) and h(x)=log(e)x...

Let`f(x)=sinx,g(x)=x^(2)` and `h(x)=log_(e)x.`
If `F(x)=("hog of ")(x)," then "F''(x)` is equal to

A

`2cosec^(3)x`

B

`2cotx^(2)-4x^(2)cosec^(2)x^(2)`

C

`2xcotx^(2)`

D

`-2cosec^(2)x`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`F(x)=("hofog")(x)`
`implies" "F(x)=h{g(f(x))}=h{g(sinx)}=h(sin^(2)x)`
`implies" "F(x)=log_(e)sin^(2)x=2log_(e)sinx`
`:." "F'(x)=2cotx" and "f''(x)=-2cosec^(2)x`
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