Question

If $f\left(x^5\right)=5x^3$, then $f^{\prime }\left(x\right)=$

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

Answer 1

The correct option is A $\frac{3}{\sqrt[5]{5x^2}}$

Given $f\left(x^5\right)=5x^3$

Replacing $x^5$ by $x$, we get $f\left(x\right)=5x^{3/5}$

Derivative of new $f$ will be $f^{{}^{\prime }}=5\times 3/5\times x^{3/5-1}$ $=3x^{-2/5}$

option A is correct answer.