What is the derivative of \sqrt[3]{(3x)/(9x-8)} ?

The derivative of \sqrt[3]{(3x)/(9x-8)} is -8/(3^{2/3)x^{2/3}(9x-8)^{4/3}}

What is the first derivative of \sqrt[3]{(3x)/(9x-8)} ?

The first derivative of \sqrt[3]{(3x)/(9x-8)} is -8/(3^{2/3)x^{2/3}(9x-8)^{4/3}}

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derivative of

- \frac{8}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( 9 x - 8 ) ^{\frac{4}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( \frac{3 x}{9 x - 8} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{3 x}{9 x - 8})

= \frac{1}{3 ( \frac{3 x}{9 x - 8} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{3 x}{9 x - 8})

\frac{d}{d x} (\frac{3 x}{9 x - 8}) = - \frac{24}{( 9 x - 8 ) ^{2}}

= \frac{1}{3 ( \frac{3 x}{9 x - 8} ) ^{\frac{2}{3}}} (- \frac{24}{( 9 x - 8 ) ^{2}})

Simplify

\frac{1}{3 ( \frac{3 x}{9 x - 8} ) ^{\frac{2}{3}}} (- \frac{24}{( 9 x - 8 ) ^{2}}) : - \frac{8}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( 9 x - 8 ) ^{\frac{4}{3}}}

= - \frac{8}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( 9 x - 8 ) ^{\frac{4}{3}}}

\int sin^{8} (x) cos^{3} (x) d x

\int_{- \infty}^{0} 4^{x} d x

y = x \cdot e^{x}

\int \frac{15}{1 - cos ( 3 x )} d x

\frac{d}{d x} (357 x + 45 (x + \frac{1}{x})^{3})

What is the derivative of \sqrt[3]{(3x)/(9x-8)} ?
The derivative of \sqrt[3]{(3x)/(9x-8)} is -8/(3^{2/3)x^{2/3}(9x-8)^{4/3}}
What is the first derivative of \sqrt[3]{(3x)/(9x-8)} ?
The first derivative of \sqrt[3]{(3x)/(9x-8)} is -8/(3^{2/3)x^{2/3}(9x-8)^{4/3}}