A) \[\frac{3}{\sqrt[5]{{{x}^{2}}}}\]
B) \[\frac{3}{\sqrt[5]{x}}\]
C) \[\frac{3}{x}\]
D) \[\sqrt[5]{x}\]
Correct Answer: A
Solution :
Given, \[f({{x}^{5}})=5{{x}^{3}}\] 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 \[f'(x)=5.\frac{3}{5}{{x}^{-2/5}}\] \[=\frac{3}{\sqrt[5]{{{x}^{2}}}}\]
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