What is the derivative of ((x+1(x+2))/((x-1)(x-2))) ?

The derivative of ((x+1(x+2))/((x-1)(x-2))) is (-6x^2+12)/((x-1)^2(x-2)^2)

What is the first derivative of ((x+1(x+2))/((x-1)(x-2))) ?

The first derivative of ((x+1(x+2))/((x-1)(x-2))) is (-6x^2+12)/((x-1)^2(x-2)^2)

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

\frac{- 6 x ^{2} + 12}{( x - 1 ) ^{2} ( x - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{- 6 x ^{2} + 12}{( x - 1 ) ^{2} ( x - 2 ) ^{2}}

\frac{\partial}{\partial x} (4 x^{3} + 2 x y^{2} + 1)

\int x^{2} arctan (4 x) d x

\frac{d}{d x} (- 15)

\frac{\partial}{\partial y} (sin (4 y) e^{- 5 x})

\frac{d}{d x} (\frac{x ^{7} - 4 x ^{3} + 12 x}{x ^{3}})

What is the derivative of ((x+1(x+2))/((x-1)(x-2))) ?
The derivative of ((x+1(x+2))/((x-1)(x-2))) is (-6x^2+12)/((x-1)^2(x-2)^2)
What is the first derivative of ((x+1(x+2))/((x-1)(x-2))) ?
The first derivative of ((x+1(x+2))/((x-1)(x-2))) is (-6x^2+12)/((x-1)^2(x-2)^2)