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Find the derivative of each function.$$f(x)=\sqrt{\left(x^{2}+1\right)(\sqrt{x}+1)^{3}}$$

$\frac{(\sqrt{x}+1)^{2}\left[4 x^{\frac{3}{2}}(\sqrt{x}+1)+3\left(x^{2}+1\right)\right]}{4 \sqrt{x} \sqrt{\left(x^{2}+1\right)(\sqrt{x}+1)}}$

Calculus 1 / AB

Chapter 2

Differentiation

Section 5

The Chain Rule

Derivatives

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this time they want us to take the derivative of the following function we have. Rex is equal to the square of X squared, plus one times the square root of X plus one. Cute. Yeah, And so we end up with Let's see, let me take our derivative. We have 1/2 times the input X squared plus one Times square directs plus one cube all of that to the negative 1/2 power and I'm gonna multiply by literally of the inside. But that's gonna be a product will well to x. Then leave the second Tamerlan X squared plus one cubed. And this time, do the reverse. Leave the first term alone, but take the derivative of the second. This one will require General square root of X plus one. That's the inputs word and times the derivative of that. Well, what's in? Let's put that way in the friend. So we'll have close one Health X to the negative one. Help! Yeah, this is our derivative. We could simplify it, but it looks good

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