What is the derivative of (x-5/((x-3)(x-1))) ?

The derivative of (x-5/((x-3)(x-1))) is (-x^2+10x-17)/((x-3)^2(x-1)^2)

What is the first derivative of (x-5/((x-3)(x-1))) ?

The first derivative of (x-5/((x-3)(x-1))) is (-x^2+10x-17)/((x-3)^2(x-1)^2)

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\frac{d}{d x} (\frac{x - 5}{( x - 3 ) ( x - 1 )})

\frac{- x ^{2} + 10 x - 17}{( x - 3 ) ^{2} ( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{( x - 3 ) ( x - 1 )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x - 3 ) ( x - 1 ) - \frac{d}{d x} ( ( x - 3 ) ( x - 1 ) ) ( x - 5 )}{( ( x - 3 ) ( x - 1 ) ) ^{2}}

\frac{d}{d x} (x - 5) = 1

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

= \frac{1 \cdot ( x - 3 ) ( x - 1 ) - ( 2 x - 4 ) ( x - 5 )}{( ( x - 3 ) ( x - 1 ) ) ^{2}}

Simplify

\frac{1 \cdot ( x - 3 ) ( x - 1 ) - ( 2 x - 4 ) ( x - 5 )}{( ( x - 3 ) ( x - 1 ) ) ^{2}} : \frac{- x ^{2} + 10 x - 17}{( x - 3 ) ^{2} ( x - 1 ) ^{2}}

= \frac{- x ^{2} + 10 x - 17}{( x - 3 ) ^{2} ( x - 1 ) ^{2}}

What is the derivative of (x-5/((x-3)(x-1))) ?
The derivative of (x-5/((x-3)(x-1))) is (-x^2+10x-17)/((x-3)^2(x-1)^2)
What is the first derivative of (x-5/((x-3)(x-1))) ?
The first derivative of (x-5/((x-3)(x-1))) is (-x^2+10x-17)/((x-3)^2(x-1)^2)