Isaac H.

asked • 06/26/23

Prove that: d/dx (cosh^(-1) x) = (1/√(x^2 - 1))

Problem #1. Prove that:


d/dx (cosh-1 x) = (1/√(x2 - 1))


Problem #2. Evaluate the derivative:


d/dx [cosh(ln x)]


Problem #3. Compute the definite integral:


∫10 (1/√(16x2 + 1)) dx

Doug C.

Might do a video for problem 1, but here is a Desmos graph that gives some hints for problem 3 (trig substitution). desmos.com/calculator/hcts9lvwmm Problem 2 is straightforward since the derivative of cosh(x) is sinh(x). Then use the chain rule (multiplying sinh(ln(x)) by derivative of ln(x).
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06/27/23

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Doug C. answered • 06/27/23

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Isaac H.

This video hasn't fully loaded for me to watch yet.
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06/27/23

Doug C.

Yes, I know, I have a case opened with WyzAnt support. Here is what I will do in the meantime. Post a picture of the solution on Desmos and provide the link here.
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06/27/23

Doug C.

Here is the link, not quite as detailed explanation as the video, but hopefully you can follow along. Select the URL, right-click, and choose go-to... to visit the link: desmos.com/calculator/jlvdyxzwz2
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06/27/23

Isaac H.

Thank you very much for your help!
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06/27/23

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