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}}

\int \frac{10 x ^{2} - 9 x + 4}{x ( x ^{2} + 4 )} d x

2 x + 5, x^{2} + 2 x + 1

\int \frac{1}{( x + 6 ) ( x + 8 )} d x

\int_{0}^{5} \frac{1}{x ^{\frac{11}{12}}} d x

\frac{d}{d x} (6 - 5 cos (\frac{π}{15} x))

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)