A) \[\frac{1}{2(1+x)\sqrt{x}}\]
B) \[\frac{3}{(1+x)\sqrt{x}}\]
C) \[\frac{2}{(1+x)\sqrt{x}}\]
D) \[\frac{3}{2(1-x)\sqrt{x}}\]
E) \[\frac{3}{2(1+x)\sqrt{x}}\]
Correct Answer: E
Solution :
Let \[y={{\tan }^{-1}}\left\{ \frac{3\sqrt{x}-{{x}^{3/2}}}{1-3x} \right\}\] Again let \[\sqrt{x}=\tan t\] \[\therefore \]\[y={{\tan }^{-1}}\left\{ \frac{3\tan t-{{\tan }^{3}}t}{1-3{{\tan }^{2}}t} \right\}={{\tan }^{-1}}(\tan 3t)\] \[\Rightarrow \] \[y=3{{\tan }^{-1}}\sqrt{x}\] On differentiating, we get \[\frac{dy}{dx}=\frac{3}{1+x}.\frac{1}{2\sqrt{x}}=\frac{3}{2(1+x)\sqrt{x}}\]
You need to login to perform this action.
You will be redirected in
3 sec
