What is the derivative of (x^2-2x)/(x+1) ?

The derivative of (x^2-2x)/(x+1) is (x^2+2x-2)/((x+1)^2)

What is the first derivative of (x^2-2x)/(x+1) ?

The first derivative of (x^2-2x)/(x+1) is (x^2+2x-2)/((x+1)^2)

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derivative of

\frac{x ^{2} - 2 x}{x + 1}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x + 1) = 1

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

Simplify

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

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

y = - x

- 3 sin (5 t)

\frac{d x}{d y} = - \frac{1}{7} x

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

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

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