What is the derivative of \sqrt[3]{(3x/(6x-5)}) ?

The derivative of \sqrt[3]{(3x/(6x-5)}) is -5/(3^{2/3)x^{2/3}(6x-5)^{4/3}}

What is the first derivative of \sqrt[3]{(3x/(6x-5)}) ?

The first derivative of \sqrt[3]{(3x/(6x-5)}) is -5/(3^{2/3)x^{2/3}(6x-5)^{4/3}}

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- \frac{5}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( 6 x - 5 ) ^{\frac{4}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( \frac{3 x}{6 x - 5} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{3 x}{6 x - 5})

= \frac{1}{3 ( \frac{3 x}{6 x - 5} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{3 x}{6 x - 5})

\frac{d}{d x} (\frac{3 x}{6 x - 5}) = - \frac{15}{( 6 x - 5 ) ^{2}}

= \frac{1}{3 ( \frac{3 x}{6 x - 5} ) ^{\frac{2}{3}}} (- \frac{15}{( 6 x - 5 ) ^{2}})

Simplify

\frac{1}{3 ( \frac{3 x}{6 x - 5} ) ^{\frac{2}{3}}} (- \frac{15}{( 6 x - 5 ) ^{2}}) : - \frac{5}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( 6 x - 5 ) ^{\frac{4}{3}}}

= - \frac{5}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( 6 x - 5 ) ^{\frac{4}{3}}}

What is the derivative of \sqrt[3]{(3x/(6x-5)}) ?
The derivative of \sqrt[3]{(3x/(6x-5)}) is -5/(3^{2/3)x^{2/3}(6x-5)^{4/3}}
What is the first derivative of \sqrt[3]{(3x/(6x-5)}) ?
The first derivative of \sqrt[3]{(3x/(6x-5)}) is -5/(3^{2/3)x^{2/3}(6x-5)^{4/3}}