SOLVED: Do the reverse chain rule: (.2 4

Chain Rule For Finding Derivatives
Chain Rule For Finding Derivatives

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Do the reverse chain rule:
(.2 4 | c +1) dx

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00:21

Find an antiderivative by reversing the chain rule, product rule or quotient rule.$$\int 2 x \cos x^{2} d x$$

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Find an antiderivative by reversing the chain rule, product rule or quotient rule.$$\int x^{2} \sqrt{x^{3}+2} d x$$

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Find an antiderivative by reversing the chain rule, product rule or quotient rule.$$\int \frac{x \cos x^{2}}{\sqrt{\sin x^{2}}} d x$$

02:22

Find an antiderivative by reversing the chain rule, product rule or quotient rule.$$\int\left(x \sin 2 x+x^{2} \cos 2 x\right) d x$$

00:33

Use Version 1 of the Chain Rule to calculate $\frac{d y}{d x}$.$$y=e^{-x^{2}}$$

Transcript

to evaluate the definite integral from 0 to 1 of x times expert. Plus one raised to the fourth power dx. We have to do the reverse chain rule. Now the reverse of chain rule for anti derivatives is the substitution technique. So in this case we first want to let U equal to the inner function X squared plus one. And then you will take the derivative of you. You have a differential of U equal to two x. DX. And since you only have X. Dx then you have to divide both sides by two. We have one half the U equal to X. Dx. And then since our limits are in terms of X. And we have to change it both of them to be in terms of you, If…

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