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

The derivative of

Starting with:

use the chain rule to get:

use the chain rule once again on the remaining derivative:

Simplify:

Finally:

If you have any questions about the use of the chain rule or any other part of this solution, then please ask.

Rory.

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To find the derivative of (-\ln(x-(x^2+1)^{1/2})), you can apply the chain rule and the derivative of the natural logarithm function. The derivative is:

[ \frac{d}{dx}\left(-\ln(x-(x^2+1)^{1/2})\right) = -\frac{1}{x-(x^2+1)^{1/2}} \times \left(1 - \frac{1}{2}(x^2+1)^{-\frac{1}{2}}(2x)\right) ]

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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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