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Popular >

derivative of (2x^2+x+9^{-3})

Solution

\frac{d}{d x} ((2 x^{2} + x + 9)^{- 3})

Solution

- \frac{3 ( 4 x + 1 )}{( 2 x ^{2} + x + 9 ) ^{4}}

Solution steps

\frac{d}{d x} ((2 x^{2} + x + 9)^{- 3})

Apply the chain rule:

- \frac{3}{( 2 x ^{2} + x + 9 ) ^{4}} \frac{d}{d x} (2 x^{2} + x + 9)

= - \frac{3}{( 2 x ^{2} + x + 9 ) ^{4}} \frac{d}{d x} (2 x^{2} + x + 9)

\frac{d}{d x} (2 x^{2} + x + 9) = 4 x + 1

= - \frac{3}{( 2 x ^{2} + x + 9 ) ^{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 + 9 ) ^{4}}

Popular Examples

integral of (1-x^2)/(x+x^3)

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

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\frac{d}{d x} (5 x^{3} + 7 x^{2.5} - 3 x + 1)

limit as x approaches 0 of (7x^2-2x)/x

x \to 0 lim (\frac{7 x ^{2} - 2 x}{x})

integral of (4/x+x/4)

\int (\frac{4}{x} + \frac{x}{4}) d x

derivative of 11xe^x derivative of

11 x e^{x}

Frequently Asked Questions (FAQ)

What is the derivative of (2x^2+x+9^{-3}) ?
The derivative of (2x^2+x+9^{-3}) is -(3(4x+1))/((2x^2+x+9)^4)
What is the first derivative of (2x^2+x+9^{-3}) ?
The first derivative of (2x^2+x+9^{-3}) is -(3(4x+1))/((2x^2+x+9)^4)