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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \frac{d y}{d x} + 2 y = 10 x^{2}

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

\int \frac{3 - 6 x ^{3} + 4 x ^{6}}{x ^{6}} d x

f (x) = \frac{( 6 ln ( x ) )}{x}

\int e^{(- x)} d x

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