What is the derivative of ln((6x^2+5)/(x^{4/5)}) ?

The derivative of ln((6x^2+5)/(x^{4/5)}) is (36x^2-20)/(5x(6x^2+5))

What is the first derivative of ln((6x^2+5)/(x^{4/5)}) ?

The first derivative of ln((6x^2+5)/(x^{4/5)}) is (36x^2-20)/(5x(6x^2+5))

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derivative of

ln (\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}})

\frac{36 x ^{2} - 20}{5 x ( 6 x ^{2} + 5 )}

Solution steps

\frac{d}{d x} (ln (\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}}))

Apply the chain rule:

\frac{1}{\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}}} \frac{d}{d x} (\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}})

= \frac{1}{\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}}} \frac{d}{d x} (\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}})

\frac{d}{d x} (\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}}) = \frac{36 x ^{2} - 20}{5 x ^{\frac{9}{5}}}

= \frac{1}{\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}}} \cdot \frac{36 x ^{2} - 20}{5 x ^{\frac{9}{5}}}

Simplify

\frac{1}{\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}}} \cdot \frac{36 x ^{2} - 20}{5 x ^{\frac{9}{5}}} : \frac{36 x ^{2} - 20}{5 x ( 6 x ^{2} + 5 )}

= \frac{36 x ^{2} - 20}{5 x ( 6 x ^{2} + 5 )}

What is the derivative of ln((6x^2+5)/(x^{4/5)}) ?
The derivative of ln((6x^2+5)/(x^{4/5)}) is (36x^2-20)/(5x(6x^2+5))
What is the first derivative of ln((6x^2+5)/(x^{4/5)}) ?
The first derivative of ln((6x^2+5)/(x^{4/5)}) is (36x^2-20)/(5x(6x^2+5))