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

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

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

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

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

Solution steps

Apply the chain rule:

\frac{1}{4 ( \frac{4 x}{6 x - 5} ) ^{\frac{3}{4}}} \frac{d}{d x} (\frac{4 x}{6 x - 5})

= \frac{1}{4 ( \frac{4 x}{6 x - 5} ) ^{\frac{3}{4}}} \frac{d}{d x} (\frac{4 x}{6 x - 5})

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

= \frac{1}{4 ( \frac{4 x}{6 x - 5} ) ^{\frac{3}{4}}} (- \frac{20}{( 6 x - 5 ) ^{2}})

Simplify

\frac{1}{4 ( \frac{4 x}{6 x - 5} ) ^{\frac{3}{4}}} (- \frac{20}{( 6 x - 5 ) ^{2}}) : - \frac{5}{2 2 x ^{\frac{3}{4}} ( 6 x - 5 ) ^{\frac{5}{4}}}

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

f (x) = x^{3} - 2

\frac{d}{d x} (lo g_{4} (x^{2} - 7 x))

\int x^{2} + 9 d x

y^{^{'}} - 2 t y = 9 t^{2} e^{t^{2}}

\frac{\partial}{\partial x} (x sin (x^{2} y))

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