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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} - 12 y^{^{'}} + 61 y = 0

\frac{d y}{d x} = \frac{y}{x} ln (y)

\int_{0}^{\frac{π}{2}} - 6 sin^{2} (3 x) d x

\frac{\partial}{\partial x} (2 x y (9 - x - y))

x^{2} y^{2}

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