What is the derivative of ((4x+1/(2-5x))^{1/3}) ?

The derivative of ((4x+1/(2-5x))^{1/3}) is (13)/(3(4x+1)^{2/3)(-5x+2)^{4/3}}

What is the first derivative of ((4x+1/(2-5x))^{1/3}) ?

The first derivative of ((4x+1/(2-5x))^{1/3}) is (13)/(3(4x+1)^{2/3)(-5x+2)^{4/3}}

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\frac{d}{d x} ((\frac{4 x + 1}{2 - 5 x})^{\frac{1}{3}})

\frac{13}{3 ( 4 x + 1 ) ^{\frac{2}{3}} ( - 5 x + 2 ) ^{\frac{4}{3}}}

Solution steps

\frac{d}{d x} ((\frac{4 x + 1}{2 - 5 x})^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( \frac{4 x + 1}{2 - 5 x} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{4 x + 1}{2 - 5 x})

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

\frac{d}{d x} (\frac{4 x + 1}{2 - 5 x}) = \frac{13}{( 2 - 5 x ) ^{2}}

= \frac{1}{3 ( \frac{4 x + 1}{2 - 5 x} ) ^{\frac{2}{3}}} \cdot \frac{13}{( 2 - 5 x ) ^{2}}

Simplify

\frac{1}{3 ( \frac{4 x + 1}{2 - 5 x} ) ^{\frac{2}{3}}} \cdot \frac{13}{( 2 - 5 x ) ^{2}} : \frac{13}{3 ( 4 x + 1 ) ^{\frac{2}{3}} ( - 5 x + 2 ) ^{\frac{4}{3}}}

= \frac{13}{3 ( 4 x + 1 ) ^{\frac{2}{3}} ( - 5 x + 2 ) ^{\frac{4}{3}}}

f (x) = 5 x^{2} cos (x) - 4 x

y = arccos (2 x + 3)

\frac{1}{( s + 1 ) ( s - 1 ) ^{2}}

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

y = 6 8 x^{2} + 7

What is the derivative of ((4x+1/(2-5x))^{1/3}) ?
The derivative of ((4x+1/(2-5x))^{1/3}) is (13)/(3(4x+1)^{2/3)(-5x+2)^{4/3}}
What is the first derivative of ((4x+1/(2-5x))^{1/3}) ?
The first derivative of ((4x+1/(2-5x))^{1/3}) is (13)/(3(4x+1)^{2/3)(-5x+2)^{4/3}}