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Find the derivative of each function.$$f(x)=\sqrt{\frac{x}{x^{2}+1}}$$

$=\frac{1-x^{2}}{2 \sqrt{x}\left(x^{2}+1\right)^{3 / 2}}$

Calculus 1 / AB

Chapter 2

Differentiation

Section 5

The Chain Rule

Derivatives

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Vega was the function Apple X is equal to the square root of X over X squared plus one. Well, lets him take their a tive on the to do 1/2 of the input. So enough times X x crib plus one and then document the power. It's not a negative one. But now when you take that area of the inside and this will require a question room the ruler of the top times the bottom so x squared plus one and minus this time leave the top alone times the derivative of the bomb, We'll end up with two X. Does that look right? Mm. Yeah, they're the bottom is two X and not all over the bottom square. Well, this is minus two X squared, so end up with a one minus x squared on the number, and that isn't I hate cancels with anything in the bottom so we could leave our and say like this. Um, it looks good.

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