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Derive the function ln((((3x+2)^5)/(x^4+7))^0.5) with respect to x

\frac{d}{dx}\left(\ln\left(\sqrt{\frac{\left(3x+2\right)^5}{x^4+7}}\right)\right)

Step by step solution

Problem

$\frac{d}{dx}\left(\ln\left(\sqrt{\frac{\left(3x+2\right)^5}{x^4+7}}\right)\right)$

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Answer

$\frac{1}{2}\left(\frac{15\left(2+3x\right)^{4}\left(7+x^4\right)-4\left(2+3x\right)^5x^{3}}{\left(2+3x\right)^{5}\left(7+x^4\right)}\right)$

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Problem Stats

Main topic:

Differential calculus

Used formulas:

7

Time to solve it:

0.93 seconds

Views:

128