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

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

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

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

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derivative of

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

Solution steps

Apply the chain rule:

\frac{1}{5 ( \frac{5 x}{4 x - 3} ) ^{\frac{4}{5}}} \frac{d}{d x} (\frac{5 x}{4 x - 3})

= \frac{1}{5 ( \frac{5 x}{4 x - 3} ) ^{\frac{4}{5}}} \frac{d}{d x} (\frac{5 x}{4 x - 3})

\frac{d}{d x} (\frac{5 x}{4 x - 3}) = - \frac{15}{( 4 x - 3 ) ^{2}}

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

Simplify

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

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

900 x - \frac{1}{3} x^{3} + 2500

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\int_{0}^{1} e^{x} + e^{- x} d x

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