Question

Let $ f(x)=\sin x,g(x)={{x}^{2}} $ and $ h(x)={{\log }_{e}}x $ . If $ f(x)=(hogof)(x), $ then $ f(x) $ is equal to

• A. $ a\cos e{{c}^{3}}x $
• B. $ a\cot {{x}^{2}}-4{{x}^{2}}\cos e{{c}^{2}}{{x}^{2}} $
• C. $ 2x\cot {{x}^{2}} $
• D. $ -2\cos e{{c}^{2}}x $
• E. $ 4\cos e{{c}^{2}}x $

Answer 1

Answer: (D)

Given, $ f(x)=\sin x,g(x)={{x}^{2}} $ and $ h(x)={{\log }_{e}}x $
Also, $ f(x)=(hogof)(x) $
Now, $ [hog](x)=2{{\log }_{e}}x $
$ \Rightarrow $ $ (hogof)(x)=2{{\log }_{e}}x $
$ \Rightarrow $ $ f(x)=2{{\log }_{e}}\sin x $
On differentiating w.r.t. $ x, $
we get $ f(x)=2\cot x $
Again differentiating,
we get $ f(x)=-2\cos e{{c}^{2}}x $