What is the derivative of ((x^2-5x)/(x-2)) ?

The derivative of ((x^2-5x)/(x-2)) is (x^2-4x+10)/((x-2)^2)

What is the first derivative of ((x^2-5x)/(x-2)) ?

The first derivative of ((x^2-5x)/(x-2)) is (x^2-4x+10)/((x-2)^2)

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

\frac{x ^{2} - 4 x + 10}{( x - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{x ^{2} - 4 x + 10}{( x - 2 ) ^{2}}

\frac{x ^{2}}{5 + 2 x}

(x^{2} - 1)^{3}

\frac{s}{( s ^{2} - 1 ) ^{2}}

\frac{d}{d x} (- ln^{4} (2 sin^{2} (x)^{3} - 1))

x y^{^{'}} = \frac{1}{x y}

What is the derivative of ((x^2-5x)/(x-2)) ?
The derivative of ((x^2-5x)/(x-2)) is (x^2-4x+10)/((x-2)^2)
What is the first derivative of ((x^2-5x)/(x-2)) ?
The first derivative of ((x^2-5x)/(x-2)) is (x^2-4x+10)/((x-2)^2)