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

The derivative of (x-2)/((x+2)(x-3)) is (-x^2+4x-8)/((x+2)^2(x-3)^2)

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

The first derivative of (x-2)/((x+2)(x-3)) is (-x^2+4x-8)/((x+2)^2(x-3)^2)

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derivative of

\frac{x - 2}{( x + 2 ) ( x - 3 )}

\frac{- x ^{2} + 4 x - 8}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x + 2 ) ( x - 3 ) - ( 2 x - 1 ) ( x - 2 )}{( ( x + 2 ) ( x - 3 ) ) ^{2}} : \frac{- x ^{2} + 4 x - 8}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

= \frac{- x ^{2} + 4 x - 8}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

What is the derivative of (x-2)/((x+2)(x-3)) ?
The derivative of (x-2)/((x+2)(x-3)) is (-x^2+4x-8)/((x+2)^2(x-3)^2)
What is the first derivative of (x-2)/((x+2)(x-3)) ?
The first derivative of (x-2)/((x+2)(x-3)) is (-x^2+4x-8)/((x+2)^2(x-3)^2)