Question

Find $f^{\prime }\left(x\right)$ of $f\left(x\right)$
if $f\left(x\right)$ is given by
(i) $x{e}^x$
(ii) $x\sin x$

• A. (i)$\to (x+1)e^x$
  (ii)$\to x\cos x+\sin x$
• B. (i)$\to (x-1)e^x$
  (ii)$\to \cos x+\sin x$
• C. (i)$\to (x-1)e^x$
  (ii)$\to x^2.\cos x+\sin x$
• D. (i)$\to (x+1)e^{2x}$
  (ii)$\to x.\cos x+{\sin }^{2}x$

Answer 1

The correct option is A (i)$\to (x+1)e^x$

(ii)$\to x\cos x+\sin x$
(i) $f^{\prime }\left(x\right)=x{e}^x+e^x.1=(x+1)e^x$
(ii) $f^{\prime }\left(x\right)=x.\frac{d}{dx}\left(sinx\right)+sinx.\frac{d}{dx}\left(x\right)$ $f^{\prime }\left(x\right)=x.cosx+sinx$