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Popular >

derivative of (2x^2-7)^{-1}

Solution

derivative of

(2 x^{2} - 7)^{- 1}

Solution

- \frac{4 x}{( 2 x ^{2} - 7 ) ^{2}}

Solution steps

\frac{d}{d x} ((2 x^{2} - 7)^{- 1})

Apply the chain rule:

- \frac{1}{( 2 x ^{2} - 7 ) ^{2}} \frac{d}{d x} (2 x^{2} - 7)

= - \frac{1}{( 2 x ^{2} - 7 ) ^{2}} \frac{d}{d x} (2 x^{2} - 7)

\frac{d}{d x} (2 x^{2} - 7) = 4 x

= - \frac{1}{( 2 x ^{2} - 7 ) ^{2}} \cdot 4 x

Simplify

- \frac{1}{( 2 x ^{2} - 7 ) ^{2}} \cdot 4 x : - \frac{4 x}{( 2 x ^{2} - 7 ) ^{2}}

= - \frac{4 x}{( 2 x ^{2} - 7 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (2x^2-7)^{-1} ?
The derivative of (2x^2-7)^{-1} is -(4x)/((2x^2-7)^2)
What is the first derivative of (2x^2-7)^{-1} ?
The first derivative of (2x^2-7)^{-1} is -(4x)/((2x^2-7)^2)