# Suppose that f : R → R is differentiable and define g(x) = x^3 f(x^3). Show that g is differentiable and compute g′

Question
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Suppose that f : R → R is differentiable and define g(x) = x^3 f(x^3). Show that g is differentiable and compute g′

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Step 1

Given:

The function f : R → R is differentiable.

The function g(x) = x3 f(x3).

Step 2

Proof:

It is known that  x3  is differentiable, then by the given it can be stated that f(x3) is also differenitable.

Now show that x3 f(x3) 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 =  x3 f(x3) is differentiable.

Step 3

Calculation:

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

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