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Popular >

derivative of (2x^2+x+1)^{-3}

Solution

derivative of

(2 x^{2} + x + 1)^{- 3}

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

Popular Examples

\frac{d a}{d a}

(dy)/(dt)=((2y^4+t^4))/(ty^3)

\frac{d y}{d t} = \frac{( 2 y ^{4} + t ^{4} )}{t y ^{3}}

(dy)/(dt)+20 6/5-6/5 e^{-20t}=24

\frac{d y}{d t} + 20 \frac{6}{5} - \frac{6}{5} e^{- 20 t} = 24

integral of (tan^2(x))/(sec(x))

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

limit as x approaches 0 of (e^{9x}-1)/x

x \to 0 lim (\frac{e ^{9 x} - 1}{x})

Frequently Asked Questions (FAQ)

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