Question

Given $f\left(x\right)=\frac{sinx}{x}$. Find f'(x).

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

If a function is of form f(x)=$\frac{g\left(x\right)}{h\left(x\right)}$,
Then f'(x)= $\frac{\frac{\left(h\right(x\left)\right)d\left(g\right(x\left)\right)}{dx}-g\left(x\right)\frac{d\left(h\right(x\left)\right)}{dx}}{\left(h\right(x){)}^2}$

Therefore, here,g(x)=sinx,h(x)=x.
$\Rightarrow$ f '(X)= x$\frac{\frac{d\left(sinx\right)}{dx}-sinx\frac{d\left(x\right)}{dx}}{(x{)}^2}$ = $x\frac{x\left(cosx\right)-sinx}{(x{)}^2}$
$\therefore$ f '(x) = $\frac{xcosx-sinx}{x^2}$