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

The derivative of (x^2+2x/(4-5x)) is (-5x^2+8x+8)/((4-5x)^2)

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

The first derivative of (x^2+2x/(4-5x)) is (-5x^2+8x+8)/((4-5x)^2)

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

\frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (4 - 5 x) = - 5

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

Simplify

\frac{( 2 x + 2 ) ( 4 - 5 x ) - ( - 5 ) ( x ^{2} + 2 x )}{( 4 - 5 x ) ^{2}} : \frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

= \frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

What is the derivative of (x^2+2x/(4-5x)) ?
The derivative of (x^2+2x/(4-5x)) is (-5x^2+8x+8)/((4-5x)^2)
What is the first derivative of (x^2+2x/(4-5x)) ?
The first derivative of (x^2+2x/(4-5x)) is (-5x^2+8x+8)/((4-5x)^2)