- #1
(glass/2)=?
- 2
- 0
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?
Find the derivative of: f(x) = [itex](2x)^{\sqrt{2}}[/itex]
[itex]\frac{d}{dx}[/itex]x[itex]^{r}[/itex]=r[itex]^{r-1}[/itex]
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!
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!