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

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

Solution steps

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

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}}}

x \to 0 lim ([x] \cdot sin (\frac{1}{x}))

\int \frac{7 x ^{2} + 8 x - 2}{x ^{2} + 2 x} d x

z \to (2 i) lim (z^{2} - z)

f (x) = 2^{x} lo g_{2} (x)

f (x) = 6 - x, at x = 3

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}}