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Popular Calculus >

derivative of (5x^2-2x+1^{-3})

Solution

\frac{d}{d x} ((5 x^{2} - 2 x + 1)^{- 3})

Solution

- \frac{3 ( 10 x - 2 )}{( 5 x ^{2} - 2 x + 1 ) ^{4}}

Solution steps

\frac{d}{d x} ((5 x^{2} - 2 x + 1)^{- 3})

Apply the chain rule:

- \frac{3}{( 5 x ^{2} - 2 x + 1 ) ^{4}} \frac{d}{d x} (5 x^{2} - 2 x + 1)

= - \frac{3}{( 5 x ^{2} - 2 x + 1 ) ^{4}} \frac{d}{d x} (5 x^{2} - 2 x + 1)

\frac{d}{d x} (5 x^{2} - 2 x + 1) = 10 x - 2

= - \frac{3}{( 5 x ^{2} - 2 x + 1 ) ^{4}} (10 x - 2)

Multiply fractions:

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

= - \frac{3 ( 10 x - 2 )}{( 5 x ^{2} - 2 x + 1 ) ^{4}}

Graph

Popular Examples

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\int - \frac{5}{3 x} d x

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d er i v a t i v e \frac{( 2 x ^{4} + 5 x ^{3} - 2 x - 8 )}{( x + 3 )}

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y^{^{'}} = y x

Frequently Asked Questions (FAQ)

What is the derivative of (5x^2-2x+1^{-3}) ?
The derivative of (5x^2-2x+1^{-3}) is -(3(10x-2))/((5x^2-2x+1)^4)
What is the first derivative of (5x^2-2x+1^{-3}) ?
The first derivative of (5x^2-2x+1^{-3}) is -(3(10x-2))/((5x^2-2x+1)^4)