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Popular >

derivative of 4(1-x^{-2})

Solution

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

Solution

\frac{8}{( 1 - x ) ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 - x) = - 1

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

Simplify

4 (- \frac{2}{( 1 - x ) ^{3}} (- 1)) : \frac{8}{( 1 - x ) ^{3}}

= \frac{8}{( 1 - x ) ^{3}}

Popular Examples

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\frac{d}{d x} (e^{- x})

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x = y^{2}, x = y + 2 [0, 4]

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\frac{d}{d x} (x^{5} + x^{7} + x^{9})

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x \to + 2 lim (3 x - 9)

Frequently Asked Questions (FAQ)

What is the derivative of 4(1-x^{-2}) ?
The derivative of 4(1-x^{-2}) is 8/((1-x)^3)
What is the first derivative of 4(1-x^{-2}) ?
The first derivative of 4(1-x^{-2}) is 8/((1-x)^3)