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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to - 1 lim (F (x))

\int lo g_{e} (2 y + 1) d y

\int - \frac{3}{5} e^{x} d x

\int 4 - 6 x - 40 x^{3} d x

\int_{0}^{2} 1 + e^{- 2 x} d x

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