Please check this differentiation result

[cabellos]

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

my answer is:

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

is this correct?

thankyou

 

[Vagrant]

In the second part I believe the -1/2 term is outside the underroot

 

[cristo]

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

my answer is:

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

is this correct?

thankyou

You want to differentiate this: $e^{-x}(1-x)^{1/2}$? You have used the product rule correctly, but the second term is incorrect. The second term is $$e^{-x}\frac{d}{dx}(1-x)^{1/2}=e^{-x}(1-x)^{-1/2}\cdot(-\frac{1}{2})$$

Note that, when using the chain rule on the parentheses, whatever's inside the parentheses does not change.