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Popular >

derivative of (2x^2-9^{-1})

Solution

\frac{d}{d x} ((2 x^{2} - 9)^{- 1})

Solution

- \frac{4 x}{( 2 x ^{2} - 9 ) ^{2}}

Solution steps

\frac{d}{d x} ((2 x^{2} - 9)^{- 1})

Apply the chain rule:

- \frac{1}{( 2 x ^{2} - 9 ) ^{2}} \frac{d}{d x} (2 x^{2} - 9)

= - \frac{1}{( 2 x ^{2} - 9 ) ^{2}} \frac{d}{d x} (2 x^{2} - 9)

\frac{d}{d x} (2 x^{2} - 9) = 4 x

= - \frac{1}{( 2 x ^{2} - 9 ) ^{2}} \cdot 4 x

Simplify

- \frac{1}{( 2 x ^{2} - 9 ) ^{2}} \cdot 4 x : - \frac{4 x}{( 2 x ^{2} - 9 ) ^{2}}

= - \frac{4 x}{( 2 x ^{2} - 9 ) ^{2}}

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\frac{d}{d x} \frac{( x ^{2} + 32 x ^{\frac{1}{2}} )}{8}

Frequently Asked Questions (FAQ)

What is the derivative of (2x^2-9^{-1}) ?
The derivative of (2x^2-9^{-1}) is -(4x)/((2x^2-9)^2)
What is the first derivative of (2x^2-9^{-1}) ?
The first derivative of (2x^2-9^{-1}) is -(4x)/((2x^2-9)^2)