Q109 / 180 · COMEDK 2019 · Mathematics
If $f\left(x^{5}\right)=5 x^{3}$, then $f^{\prime}(x)=$
- Correct answerA$\frac{3}{\sqrt[5]{x^{2}}}$
- B$\frac{3}{\sqrt[5]{x}}$
- C$\frac{3}{x}$
- D$\sqrt[5]{x}$
Solution
We have,
$$
\begin{aligned}
f\left(x^{5}\right) &=5 x^{3} \\
\Rightarrow \quad f(x) &=5 x^{3 / 5} \\
\Rightarrow \quad f^{\prime}(x) &=5 \times \frac{3}{5} x^{\frac{3}{5}-1}=3 x^{-\frac{2}{5}} \\
&=\frac{3}{\sqrt[5]{x^{2}}}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.