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How do you find the derivative of #arcsin(x) + xsqrt(1-x^2)#?

Answer 1

Emily Ammerman

look here and reverse the process

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Answer 2

Elijah Abram

To find the derivative of ( \arcsin(x) + x\sqrt{1-x^2} ), you use the sum rule and the chain rule. The derivative of ( \arcsin(x) ) is ( \frac{1}{\sqrt{1-x^2}} ), and the derivative of ( x\sqrt{1-x^2} ) is ( \sqrt{1-x^2} + \frac{-x^2}{\sqrt{1-x^2}} ). Therefore, the derivative of the given expression is ( \frac{1}{\sqrt{1-x^2}} + \sqrt{1-x^2} - \frac{x^2}{\sqrt{1-x^2}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.