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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

` a "cosec"^(3) x `

B

`2 cot x^(2) - 4x^(2) "cosec"^(2) x^(2)`

C

` 2x cot x^(2)`

D

` 2 "cosec"^(2) x `

Text Solution

Verified by Experts

The correct Answer is:
D
`["hog"](x)= h(x^(2)) = 2 log_(e) x `
` rArr ("hogof")(x) = hog(sin x) = 2 log_(e) sin x`
` therefore F'(x) = ("hog of") (x) = 2 log_(e) sin x `
` rArr F'(x) = 2 cot x `
` rArr F'' (x) = - 2 " cosec"^(2) x `
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