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Numerade Educator

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Problem 43 Medium Difficulty

Find the derivative. Simplify where possible.
$ y = x \sinh^{-1} (x/3) - \sqrt {9 + x^2} $

Answer

$\sinh ^{-1}\left(\frac{x}{3}\right)$

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Video Transcript

we know that we're looking at one over the squared of one plus U squared is the general formula we're plugging into. Therefore, why prime as Axe Times one over the spurt of one plus acts over three squared that's obviously export over nine times 1/3 plus sign h the minus one of X over three minus acts over the square root of nine plus X squared. This simplifies to sign a TSH to the negative one of X over three in other words, 1/3 x.