Question

If $f (x^5)=5x^3$ then $f'(x)=$ is equal to

• A. $\frac {3} {\sqrt[5] {x}^2}$
• B. $\frac {3} {\sqrt[5] {x}}$
• C. $\frac {3}{x}$
• D. $ {\sqrt[5] {x}}$

Answer 1

Answer: (A)

Given, $f\left(x^{5}\right)=5 x^{3}$
Let $\,\,\,\,x^{5}=y $
$\Rightarrow \,\,\,\, x^{3}=y^{3 / 5}$
$\therefore \,\,\,\,\,\, f(y)=5 y^{3 / 5}$
or $\,\,\,f(x)=5 x^{3 / 5}$
On differentiating w.r.t. x, we get
$f'(x)=5 . \frac{3}{5} x^{-2 / 5}$
$=\frac{3}{\sqrt[5]{x^{2}}}$