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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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