# How do I find the derivative of # y=xsin^(-1)x + sqrt(1-x^2)#?

You can differentiate this function by using the product rule and the chain rule, provided that you know that

So, your function can be written like this

and

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To find the derivative of (y = x\sin^{-1}x + \sqrt{1-x^2}), we can use the sum rule and the chain rule. The derivative is (\sin^{-1}x + \frac{x}{\sqrt{1-x^2}}).

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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.

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.

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.

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- What is the derivative of #(cos x) / (1 + tan x)#?

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