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

The derivative of (x^2-3x-4)/(x-2) is (x^2-4x+10)/((x-2)^2)

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

The first derivative of (x^2-3x-4)/(x-2) is (x^2-4x+10)/((x-2)^2)

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derivative of

\frac{x ^{2} - 3 x - 4}{x - 2}

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

Solution steps

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

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

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

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

Simplify

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

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

\int 2 cos^{2} (x) sin (x) d x

\int e^{- 4 x} \cdot x d x

- \frac{3 x ^{2}}{4 y ^{2}}

2 x^{2} + 15

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

What is the derivative of (x^2-3x-4)/(x-2) ?
The derivative of (x^2-3x-4)/(x-2) is (x^2-4x+10)/((x-2)^2)
What is the first derivative of (x^2-3x-4)/(x-2) ?
The first derivative of (x^2-3x-4)/(x-2) is (x^2-4x+10)/((x-2)^2)