Practicing Success
Let $f(x)=\sin x, g(x)=2 x$ and $h(x)=\cos x$. If $\phi(x)=[go(f h)](x)$, then $\phi'' \left(\frac{\pi}{4}\right)$ is equal to |
4 0 -4 none of these |
-4 |
We have, $(f h)(x)=f(x) h(x)=\sin x \cos x$ $\phi(x)=[go(f h)](x)=g((f h)(x))$ $\Rightarrow \phi(x)=g(\sin x \cos x)=2 \sin x \cos x=\sin 2 x$ $\Rightarrow \phi'(x)=2 \cos 2 x$ $\Rightarrow \phi''(x)=-4 \sin 2 x$ $\Rightarrow \phi''(\pi / 4)=-4 \sin \pi / 2=-4$ |