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Problem simplifying a power function derivation

  • #1
Hello All,

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?

Homework Statement



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

Homework Equations



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

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!
 

Answers and Replies

  • #2
584
0
Hello if you want us to see your writing you have type[tex] then type in {/tex} but with brackets
 
  • #3
Hello if you want us to see your writing you have type[tex] then type in {/tex} but with brackets
mtayab1994, I don't exactly follow. Do you not see what I've posted? What do you mean by, "your writing"?

Thanks
 
  • #4
33,635
5,294
mtayab1994, I don't exactly follow. Do you not see what I've posted? What do you mean by, "your writing"?
I don't know what mtayab1994 was going on about - what you wrote looked perfectly clear to me.
 

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