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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral from-2 to 2 of sqrt(1+100x^2)

\int_{- 2}^{2} 1 + 100 x^{2} d x

f (x) = - cot (x)

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\int (3 x^{3} + 6 x^{2} - 12 x + 5) d x

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\frac{d}{d x} (\frac{9}{1 + 9 x})

derivative of f(x)=t^5sin(t)derivative of

f (x) = t^{5} sin (t)

Frequently Asked Questions (FAQ)

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