Expert Answer to "Find the following derivatives. ln⁡(x+3x2)" - Plainmath

Tolnaio

Answered question

2021-10-19

Find the following derivatives.

\ln (\frac{x + 3}{x^{2}})

Answer & Explanation

Layton

Skilled2021-10-20Added 89 answers

The given function is:

f (x) = \ln (\frac{x + 3}{x^{2}})

Now using property of logarithmic function:

\ln (\frac{x + 3}{x^{2}}) = \ln (x + 3) - \ln (x^{2})

\ln (\frac{x + 3}{x^{2}}) = \ln (x + 3) - 2 \ln (x)

Now the derivative of the given function is:

\frac{d}{d x} [\ln (\frac{x + 3}{x^{2}})] = \frac{d}{d x} (\ln (x + 3) - 2 \ln (x))

\frac{d}{d x} [\ln (\frac{x + 3}{x^{2}})] = \frac{d}{d x} (\ln (x + 3)) - \frac{d}{d x} (2 \ln x)

\frac{d}{d x} [\ln (\frac{x + 3}{x^{2}})] = \frac{1}{x + 3} - \frac{2}{x}

\frac{d}{d x} [\ln (\frac{x + 3}{x^{2}})] = \frac{- x - 6}{x (x + 3)}

.

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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