Double Differentiation of (e^-x)(1-x)^1/2: Correct Solutions

[cabellos]

I have to differentiate (e^-x) ((1-x)^1/2) twice:

The first time i differentiate i get

(-e^-x) ((1-x)^1/2) + (e^-x) ((1-x)^-1/2) (-1/2)

then differentiating this i get

[(e^-x) ((1-x)^1/2)] - [(e^-x) ((1-x)^-1/2) (-1/2)] + [(-1/2e^-x) (1/2(1-x)^3/2) + ((1-x)^-1/2) (1/2e^-x)]

are these correct?

thankyou for checking

 

[Dick]

If you want someone to check something for details, you should make sure you've shown what you want checked clearly and unambiguously. What does this mean '(1/2(1-x)^3/2)'? Is it (1/2)*(1-x)^(3/2)), or ((1/(2(1-x))^3)/2) etc etc. That said there should be terms with (1-x) to the power of 1/2, -1/2 and -3/2 (not 3/2). Other than that ok, I think.

 

[JANm]

First derivative is OK. Before differentiating for the second time please write the first derivative nicer by taking (1-x) out of the first term and do some adding. I am sure that simplification will result.