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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

3 x^{2} - 12 x - 15

\frac{\partial}{\partial x} (e^{- 2 t} cos (x))

\frac{d}{d x} (A (e^{x} + e^{xx}))

y^{^{''}} + 13 y^{^{'}} + 30 y = 0, y (0) = 1, y^{^{'}} (0) = 0

x \to \infty lim (\frac{5}{x} - 2)

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