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

The derivative of ((2x-1/(3x^2+x-2))^3) is (3(2x-1)^2(-6x^2+6x-3))/((3x^2+x-2)^4)

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

The first derivative of ((2x-1/(3x^2+x-2))^3) is (3(2x-1)^2(-6x^2+6x-3))/((3x^2+x-2)^4)

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

\frac{3 ( 2 x - 1 ) ^{2} ( - 6 x ^{2} + 6 x - 3 )}{( 3 x ^{2} + x - 2 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{2 x - 1}{3 x ^{2} + x - 2}) = \frac{- 6 x ^{2} + 6 x - 3}{( 3 x ^{2} + x - 2 ) ^{2}}

= 3 (\frac{2 x - 1}{3 x ^{2} + x - 2})^{2} \frac{- 6 x ^{2} + 6 x - 3}{( 3 x ^{2} + x - 2 ) ^{2}}

Simplify

3 (\frac{2 x - 1}{3 x ^{2} + x - 2})^{2} \frac{- 6 x ^{2} + 6 x - 3}{( 3 x ^{2} + x - 2 ) ^{2}} : \frac{3 ( 2 x - 1 ) ^{2} ( - 6 x ^{2} + 6 x - 3 )}{( 3 x ^{2} + x - 2 ) ^{4}}

= \frac{3 ( 2 x - 1 ) ^{2} ( - 6 x ^{2} + 6 x - 3 )}{( 3 x ^{2} + x - 2 ) ^{4}}

\int 6 sec (2 x) tan (2 x) d x

\int \frac{7 x ^{3} + 6 x}{x - 1} d x

3 x^{- 2 x}

\frac{\partial}{\partial x} (\frac{m c T}{m T})

t \to 0 lim (\frac{1}{t} - \frac{1}{e ^{t} - 1})

What is the derivative of ((2x-1/(3x^2+x-2))^3) ?
The derivative of ((2x-1/(3x^2+x-2))^3) is (3(2x-1)^2(-6x^2+6x-3))/((3x^2+x-2)^4)
What is the first derivative of ((2x-1/(3x^2+x-2))^3) ?
The first derivative of ((2x-1/(3x^2+x-2))^3) is (3(2x-1)^2(-6x^2+6x-3))/((3x^2+x-2)^4)