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

The derivative of 1/((x^2+3x+2^3)) is -(3(2x+3))/((x^2+3x+2)^4)

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

The first derivative of 1/((x^2+3x+2^3)) is -(3(2x+3))/((x^2+3x+2)^4)

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

- \frac{3 ( 2 x + 3 )}{( x ^{2} + 3 x + 2 ) ^{4}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{3}{( x ^{2} + 3 x + 2 ) ^{4}} \frac{d}{d x} (x^{2} + 3 x + 2)

= - \frac{3}{( x ^{2} + 3 x + 2 ) ^{4}} \frac{d}{d x} (x^{2} + 3 x + 2)

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

= - \frac{3}{( x ^{2} + 3 x + 2 ) ^{4}} (2 x + 3)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 ( 2 x + 3 )}{( x ^{2} + 3 x + 2 ) ^{4}}

\int cosh (d) x d x

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

\int tan (x^{2}) d x

0.0796 - 0.066 \cdot x^{\frac{1}{2}}

\int_{0}^{1} 3 (1 + x)^{5} d x

What is the derivative of 1/((x^2+3x+2^3)) ?
The derivative of 1/((x^2+3x+2^3)) is -(3(2x+3))/((x^2+3x+2)^4)
What is the first derivative of 1/((x^2+3x+2^3)) ?
The first derivative of 1/((x^2+3x+2^3)) is -(3(2x+3))/((x^2+3x+2)^4)