Solved: "Derivatives of logarithmic functions Calculate the derivative of..."

Elleanor Mckenzie

Answered question

2021-10-20

Derivatives of logarithmic functions Calculate the derivative of the following functions

y = 4 \log_{3} (x^{2} - 1)

Talisha

Skilled2021-10-21Added 93 answers

Step 1 Given logarithmic function

y = 4 \log_{3} (x^{2} - 1)

Step 2 Formula

\frac{d}{d x} (\log x) = \frac{1}{x} \frac{d}{d x} (x) = \frac{1}{x}

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

\frac{d}{d x} (4 \log (x^{2} - 1))

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

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

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

Step 4 Answer

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

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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