What is the solution for derivative of f(1/3 x^3)=2x^5 ?

The solution for derivative of f(1/3 x^3)=2x^5 is f(x)=x^3+(c_{1})/(x^3)

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derivative of f(1/3 x^3)=2x^5

\frac{d}{d x} (f (\frac{1}{3} x^{3})) = 2 x^{5}

f (x) = x^{3} + \frac{c _{1}}{x ^{3}}

Solution steps

\frac{d}{d x} (f (x) (\frac{1}{3} x^{3})) = 2 x^{5}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) \frac{1}{3} x^{3} = \int 2 x^{5} d x

\int 2 x^{5} d x = \frac{x ^{6}}{3} + c_{1}

f (x) \frac{1}{3} x^{3} = \frac{x ^{6}}{3} + c_{1}

Isolate

f (x) : f (x) = x^{3} + \frac{3 c _{1}}{x ^{3}}

f (x) = x^{3} + \frac{3 c _{1}}{x ^{3}}

Simplify

f (x) = x^{3} + \frac{c _{1}}{x ^{3}}

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What is the solution for derivative of f(1/3 x^3)=2x^5 ?
The solution for derivative of f(1/3 x^3)=2x^5 is f(x)=x^3+(c_{1})/(x^3)