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

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

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

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

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derivative of

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

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{4 x}{4 x - 3}) = - \frac{12}{( 4 x - 3 ) ^{2}}

= \frac{1}{4 ( \frac{4 x}{4 x - 3} ) ^{\frac{3}{4}}} (- \frac{12}{( 4 x - 3 ) ^{2}})

Simplify

\frac{1}{4 ( \frac{4 x}{4 x - 3} ) ^{\frac{3}{4}}} (- \frac{12}{( 4 x - 3 ) ^{2}}) : - \frac{3}{2 2 x ^{\frac{3}{4}} ( 4 x - 3 ) ^{\frac{5}{4}}}

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

\frac{\partial}{\partial x} (ln (\frac{x}{y}))

\int_{- a}^{a} e^{\frac{- x ^{2}}{a ^{2}}} d x

(- 4, 3), (3, 1)

\int \frac{x ^{2} - 15}{x + 7} d x

y^{^{''}} - 2 y^{^{'}} = 9 x

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