# How do you differentiate #y=ssqrt(1-s^2)+arccoss#?

Next, to apply the product rule to find the overall derivative.

When you find a common denominator by algebraic manipulation, hence:

The simplification of the two together is quite delightful, as the already have the same denominator - so you can just add!

Sorry for all the confusion here, I hope it helps!

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To differentiate (y = s\sqrt{1 - s^2} + \arccos(s)), apply the chain rule and the derivatives of square root and arccosine functions.

(y' = \frac{d}{ds}[s\sqrt{1 - s^2}] + \frac{d}{ds}[\arccos(s)])

(y' = \sqrt{1 - s^2} + \frac{-1}{\sqrt{1 - s^2}})

(y' = \frac{\sqrt{1 - s^2} - 1}{\sqrt{1 - s^2}})

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