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I can compute the solution, but I fail to see how it further simplifies into the final expression. The solution manual lists both the answer and its simplified formulation.

How do I go from step three to step four?

1. The problem statement, all variables and given/known data

Find the derivative of: f(x) = [itex](2x)^{\sqrt{2}}[/itex]

2. Relevant equations

[itex]\frac{d}{dx}[/itex]x[itex]^{r}[/itex]=r[itex]^{r-1}[/itex]

3. The attempt at a solution

1) f(x) = [itex](2x)^{\sqrt{2}}[/itex] = ([itex]2^{\sqrt{2}}[/itex])([itex]x^{\sqrt{2}}[/itex])

2) Application of the product rule: g'(x)f(x) + f'(x)g(x)

3) Answer = [itex]2^{\sqrt{2}}[/itex][itex]\sqrt{2}[/itex][itex]x^{\sqrt{2}-1}[/itex]

4) Simplification: [itex]2\sqrt{2}[/itex][itex](2x)^{\sqrt{2}-1}[/itex]

Many Thanks!

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# Problem simplifying a power function derivation

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