What is the derivative of (8-x+3x^2/(2-9x)) ?

The derivative of (8-x+3x^2/(2-9x)) is (-27x^2+12x+70)/((2-9x)^2)

What is the first derivative of (8-x+3x^2/(2-9x)) ?

The first derivative of (8-x+3x^2/(2-9x)) is (-27x^2+12x+70)/((2-9x)^2)

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\frac{d}{d x} (\frac{8 - x + 3 x ^{2}}{2 - 9 x})

\frac{- 27 x ^{2} + 12 x + 70}{( 2 - 9 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 - x + 3 x ^{2}}{2 - 9 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 - x + 3 x ^{2} ) ( 2 - 9 x ) - \frac{d}{d x} ( 2 - 9 x ) ( 8 - x + 3 x ^{2} )}{( 2 - 9 x ) ^{2}}

\frac{d}{d x} (8 - x + 3 x^{2}) = 6 x - 1

\frac{d}{d x} (2 - 9 x) = - 9

= \frac{( 6 x - 1 ) ( 2 - 9 x ) - ( - 9 ) ( 8 - x + 3 x ^{2} )}{( 2 - 9 x ) ^{2}}

Simplify

\frac{( 6 x - 1 ) ( 2 - 9 x ) - ( - 9 ) ( 8 - x + 3 x ^{2} )}{( 2 - 9 x ) ^{2}} : \frac{- 27 x ^{2} + 12 x + 70}{( 2 - 9 x ) ^{2}}

= \frac{- 27 x ^{2} + 12 x + 70}{( 2 - 9 x ) ^{2}}

x \to 2 lim (\frac{x + 7}{x - 2})

\frac{d}{d x} (\frac{2 x}{3 - tan ( x )})

- 3 x

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

y^{^{''}} + 4 y = - 12 cos (2 x) - 4 sin (2 x)

What is the derivative of (8-x+3x^2/(2-9x)) ?
The derivative of (8-x+3x^2/(2-9x)) is (-27x^2+12x+70)/((2-9x)^2)
What is the first derivative of (8-x+3x^2/(2-9x)) ?
The first derivative of (8-x+3x^2/(2-9x)) is (-27x^2+12x+70)/((2-9x)^2)