Question

Asked Apr 11, 2019

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Step 1

*Given:*

The function *f : R *→ *R* is differentiable.

The function g(x) =* x*^{3} *f*(*x*^{3}).

Step 2

*Proof:*

It is known that * x*^{3} is differentiable, then by the given it can be stated that *f*(*x*^{3}) is also differenitable.

Now show that* x*^{3} *f*(*x*^{3}) is differentiable.

The prduct of two differentiable function is said to be differentiable. That is, if h(x) and s(x) are two differentiable functions, then h(x)s(x) is also differentiable.

Thus, it can be concluded that g = * x*^{3} *f*(*x*^{3}) is differentiable.

Step 3

*Calculation:*

Differentiate the given g(x) with resp...

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