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

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

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

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

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

- \frac{3 ( 2 x + 1 )}{( x ^{2} + x + 1 ) ^{4}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{3}{( x ^{2} + x + 1 ) ^{4}} \frac{d}{d x} (x^{2} + x + 1)

= - \frac{3}{( x ^{2} + x + 1 ) ^{4}} \frac{d}{d x} (x^{2} + x + 1)

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

= - \frac{3}{( x ^{2} + x + 1 ) ^{4}} (2 x + 1)

Multiply fractions:

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

= - \frac{3 ( 2 x + 1 )}{( x ^{2} + x + 1 ) ^{4}}

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