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Find the derivative of the function. $ g(x) = …

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Problem 59 Hard Difficulty

Find the derivative of the function.

$ g(x) = \displaystyle \int^{3x}_{2x} \frac{u^2 - 1}{u^2 + 1} \, du $

$ \displaystyle \Biggl[ Hint: \int^{3x}_{2x} f(u) \, du = \int^0_{2x} f(u) \, du + \int^{3x}_0 f(u) \, du \Biggr] $


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Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

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Section 3

The Fundamental Theorem of Calculus

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In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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Video Transcript

Okay. Use the chain rule to find the driver of which is our goal. So what we end up with his G Prime of axe is equivalent to 27 X squared, minus three over nine X squared plus one minus eight X squared, minus two over four X squared, plus born.

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