How do I differentiate [R^2-(R-h)^2]^1/2

I think (R-h) would be just like (5-x)' as an example since R is a constant and to take the derivative of each so 5'-x' = 0-1=-1? I just dont know how to do it for this [R^2-(R-h)^2]^1/2. Would I use product rule and chain rule?

Thanks for any help!!

You are correct that differentiating R - h is similar to differentiating 5 - x in that both R and 5 are constants.

Note that √[R^2 - (R - h)^2] is not a product of two functions and that we can write this as a composite function; namely, we can write √[R^2 - (R - h)^2] = f[g(h)], where:
f(x) = √x and g(h) = R^2 - (R - h)^2.

This suggests that we should use the Chain Rule.

If we expand out R^2 - (R - h)^2, we get:
R^2 - (R^2 - 2Rh + h^2) = 2Rh - h^2.
(This will make things easier to differentiate.)

Then, differentiating yields:
d/dh √[R^2 - (R - h)^2] = d/dh √(2Rh - h^2)
= [d/dh (2Rh - h^2)] * 1/[2√(2Rh - h^2)], by the Chain and Power Rules
= (2R - 2h)/[2√(2Rh - h^2)], by differentiating and treating R like a constant
= (R - h)/√(2Rh - h^2).

I hope this helps!