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Popular >

derivative of (2x^2-4x^{-2})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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x \to 0 lim (\frac{x}{2})

Frequently Asked Questions (FAQ)

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