What is the derivative of (6x^3-5x^2-2x/(4x-3x^2)) ?

The derivative of (6x^3-5x^2-2x/(4x-3x^2)) is -(2(9x^2-24x+13))/((3x-4)^2)

What is the first derivative of (6x^3-5x^2-2x/(4x-3x^2)) ?

The first derivative of (6x^3-5x^2-2x/(4x-3x^2)) is -(2(9x^2-24x+13))/((3x-4)^2)

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\frac{d}{d x} (\frac{6 x ^{3} - 5 x ^{2} - 2 x}{4 x - 3 x ^{2}})

- \frac{2 ( 9 x ^{2} - 24 x + 13 )}{( 3 x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x ^{3} - 5 x ^{2} - 2 x}{4 x - 3 x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 6 x ^{3} - 5 x ^{2} - 2 x ) ( 4 x - 3 x ^{2} ) - \frac{d}{d x} ( 4 x - 3 x ^{2} ) ( 6 x ^{3} - 5 x ^{2} - 2 x )}{( 4 x - 3 x ^{2} ) ^{2}}

\frac{d}{d x} (6 x^{3} - 5 x^{2} - 2 x) = 18 x^{2} - 10 x - 2

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

= \frac{( 18 x ^{2} - 10 x - 2 ) ( 4 x - 3 x ^{2} ) - ( 4 - 6 x ) ( 6 x ^{3} - 5 x ^{2} - 2 x )}{( 4 x - 3 x ^{2} ) ^{2}}

Simplify

\frac{( 18 x ^{2} - 10 x - 2 ) ( 4 x - 3 x ^{2} ) - ( 4 - 6 x ) ( 6 x ^{3} - 5 x ^{2} - 2 x )}{( 4 x - 3 x ^{2} ) ^{2}} : - \frac{2 ( 9 x ^{2} - 24 x + 13 )}{( 3 x - 4 ) ^{2}}

= - \frac{2 ( 9 x ^{2} - 24 x + 13 )}{( 3 x - 4 ) ^{2}}

\frac{d}{d x} (5 x + \frac{100}{x})

x \to 2 lim (\frac{x + 2}{x - 2})

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

\frac{d}{d x} (\frac{x ^{6}}{12} ln (x) - \frac{x ^{6}}{72})

\frac{d}{d x} (e^{- 5 x} - 5 e^{- 5 x} x)

What is the derivative of (6x^3-5x^2-2x/(4x-3x^2)) ?
The derivative of (6x^3-5x^2-2x/(4x-3x^2)) is -(2(9x^2-24x+13))/((3x-4)^2)
What is the first derivative of (6x^3-5x^2-2x/(4x-3x^2)) ?
The first derivative of (6x^3-5x^2-2x/(4x-3x^2)) is -(2(9x^2-24x+13))/((3x-4)^2)