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

The derivative of (4-1/(2x^2))^{-1} is -(4x)/((8x^2-1)^2)

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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