Elleanor Mckenzie

2021-10-20

Derivatives of logarithmic functions Calculate the derivative of the following functions

$y=4{\mathrm{log}}_{3}({x}^{2}-1)$

Talisha

Skilled2021-10-21Added 93 answers

Step 1 Given logarithmic function

$y=4{\mathrm{log}}_{3}({x}^{2}-1)$

Step 2 Formula

$\frac{d}{dx}\left(\mathrm{log}x\right)=\frac{1}{x}\frac{d}{dx}\left(x\right)=\frac{1}{x}$

Step 3 We need to find the derivative of given logarithmic function

$\frac{d}{dx}\left(4\mathrm{log}({x}^{2}-1)\right)$

$=\frac{4}{{x}^{2}-1}\cdot \frac{d}{dx}({x}^{2}-1)$

$=\frac{4}{{x}^{2}-1}\cdot \left(2x\right)$

$=\frac{8x}{{x}^{2}-1}$

Step 4 Answer

$y}^{\prime}=\frac{8x}{{x}^{2}-1$

Step 2 Formula

Step 3 We need to find the derivative of given logarithmic function

Step 4 Answer

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

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