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

The derivative of ((2x+4/(3x-1))^4) is -(56(2x+4)^3)/((3x-1)^5)

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

The first derivative of ((2x+4/(3x-1))^4) is -(56(2x+4)^3)/((3x-1)^5)

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

- \frac{56 ( 2 x + 4 ) ^{3}}{( 3 x - 1 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{2 x + 4}{3 x - 1}) = - \frac{14}{( 3 x - 1 ) ^{2}}

= 4 (\frac{2 x + 4}{3 x - 1})^{3} (- \frac{14}{( 3 x - 1 ) ^{2}})

Simplify

4 (\frac{2 x + 4}{3 x - 1})^{3} (- \frac{14}{( 3 x - 1 ) ^{2}}) : - \frac{56 ( 2 x + 4 ) ^{3}}{( 3 x - 1 ) ^{5}}

= - \frac{56 ( 2 x + 4 ) ^{3}}{( 3 x - 1 ) ^{5}}

\int \frac{5 sin ( x )}{x} d x

y^{^{'}} - \frac{2}{t} y = t^{3}

\int 20 + 75 e^{- \frac{t}{50}} d t

t \cdot cos (π \cdot t)

y^{^{'}} + 2 y = 3 sin (e^{2 x})

What is the derivative of ((2x+4/(3x-1))^4) ?
The derivative of ((2x+4/(3x-1))^4) is -(56(2x+4)^3)/((3x-1)^5)
What is the first derivative of ((2x+4/(3x-1))^4) ?
The first derivative of ((2x+4/(3x-1))^4) is -(56(2x+4)^3)/((3x-1)^5)