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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derivative of

\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}}

\int [tan (5 x) + csc^{3} (3 θ)] d θ

f (x) = \frac{e ^{x}}{x}, (1, e)

\int 25 x^{2} + 4 d x

\int_{- l n (4)}^{0} 3 e^{x} d x

2 cos (x) + cos^{2} (x)

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)