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# If $f$ is continuous and $g$ and $h$ are differentiable functions, find a formula for $$\displaystyle \frac{d}{dx} \int^{h(x)}_{g(x)} f(t) \, dt$$

## $f(h(x)) \cdot h^{\prime}(x)-f(y(x)) \cdot g^{\prime}(x)$

Integrals

Integration

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

We know that if half of t is the anti derivative of lower case off of teeth and by the fundamental theme of calculus, we know half of h of acts menace off G of Axe gives us the integral from G F ax to H of X is off of DDT. Therefore, we know the derivative is gonna be just remember that you're multiplying by G prime of acts and H prime of X. Because remember these air, the chain and rules we have H and jeez, we must supply the chain rule.

#### Topics

Integrals

Integration

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp