What is the derivative of (x^2-2x+3/(x+1)) ?

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int \frac{1}{x ^{2} + 4 x + 5} d x

\int \frac{x ^{5} + x ^{2} + 2}{x ^{3} - x} d x

\int e^{- 3 x^{- 5}} x^{- 6} d x

\int sin^{3} (x) (cos^{2} (x)) d x

e^{- x}, - 0.75

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