Question

Given f(x) = g(X) . h (x) and $f^{{}^{\prime }}\left(x\right)$=$g^{{}^{\prime }}\left(x\right)$h(x) + g(x)$h^{{}^{\prime }}\left(x\right)$ find f'(x) where f(x) = x sin x.

• A. sin x - x cos x
• B. sin x + x cos x
• C. x sin x + cos x
• D. sin x + cos x

Answer 1

The correct option is B

sin x + x cos x

Given, f(x) = x sinx.

We can assume, g(x) = x and h(x) = sin x.

Therefore, $f^{{}^{\prime }}\left(x\right)$ = $g^{{}^{\prime }}\left(x\right)$ h (x) + g(x)$h^{{}^{\prime }}\left(x\right)$

= $\frac{d\left(x\right)}{dx}sinx+x.\frac{dsinx}{dx}$

Clearly, $\frac{dx}{dx}=1and\frac{d\left(sinx\right)}{dx}cosx$

$\therefore f^{{}^{\prime }}\left(x\right)=1\left(sinx\right)+x\left(cosx\right)$

$=sinx+xcosx$ .