How do you tell it to simplify and get fractional exponents?

04032017, 05:39 AM
Post: #1




How do you tell it to simplify and get fractional exponents?
I'm taking calculus 3 and we're playing with partial derivatives. I'd like the Prime to give me answers in a format that ends up in fractional exponents.
For example: \[f(x,y)=\sqrt{x^2+y^2}\] \[f_x=\frac{x}{\sqrt{x^2+y^2}}\] \[f_{xx}=\frac{y^2}{(x^2+y^2)^{\frac{3}{2}}}\] The Prime gives me: \[f_{xx}=\frac{y^{2}}{(x^{2} \sqrt{x^{2}+y^{2}}+y^{2} \sqrt{x^{2}+y^{2}})}\] If I hit that with a simplify() then a collect(), I end up with this: \[f_{xx}=\frac{y^{2}}{\sqrt{x^{2}+y^{2}} (x^{2}+y^{2})}\] Are there any CAS commands that I can use to convert that into the version with a 3/2 exponent in the denominator? I think it would be easier to use that form keep going into higher order derivatives. Thanks! 

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