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

Answer 1

Charles Anctil

#d/dx(x^2+2x-1)^(1/2)=1/2(x^2+2x-1)^(-1/2)*(2x+2)#

We may apply the power rule to obtain

#d/dx(x^2+2x-1)^(1/2)=1/2(x^2+2x-1)^(-1/2)*(2x+2)#

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Answer 2

Emily Ammerman

To find the derivative of ( \sqrt{x^2 + 2x - 1} ), use the chain rule. The derivative is:

[ \frac{d}{dx} \sqrt{x^2 + 2x - 1} = \frac{1}{2\sqrt{x^2 + 2x - 1}} \cdot \frac{d}{dx}(x^2 + 2x - 1) ]

[ = \frac{1}{2\sqrt{x^2 + 2x - 1}} \cdot (2x + 2) ]

[ = \frac{x + 1}{\sqrt{x^2 + 2x - 1}} ]

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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.