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

The derivative of ((2x+1/(3x-1))^4) is -(20(2x+1)^3)/((3x-1)^5)

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

The first derivative of ((2x+1/(3x-1))^4) is -(20(2x+1)^3)/((3x-1)^5)

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

- \frac{20 ( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (8 x^{2} cos (x) cot (x))

x \cdot e^{- x + 1}

(4, - 4), (8, - 10)

\int \frac{3 + x}{3 - x} d x

x^{^{''}} + x^{^{'}} + 3 x = 0

What is the derivative of ((2x+1/(3x-1))^4) ?
The derivative of ((2x+1/(3x-1))^4) is -(20(2x+1)^3)/((3x-1)^5)
What is the first derivative of ((2x+1/(3x-1))^4) ?
The first derivative of ((2x+1/(3x-1))^4) is -(20(2x+1)^3)/((3x-1)^5)