Question

If $f(x^5)=5x^3$ then $f^{\prime }(x)=$ 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, $f\left(x^5\right)=5x^3$
Let $x^5=y$
$\Rightarrow x^3=y^{3/5}$
$\therefore f(y)=5y^{3/5}$
or $f(x)=5x^{3/5}$
On differentiating w.r.t. x, we get
$f^{\prime }(x)=5.\frac{3}{5}{x}^{-2/5}$
$=\frac{3}{\sqrt[5]{x^2}}$