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Popular >

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

Solution

derivative of

f (x) = (2 x^{2} - 4)^{- 1}

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 8-of x/(x^2-64)

x \to 8 - lim (\frac{x}{x ^{2} - 64})

derivative of (-2x^2+9/(sqrt(9-x^2)))

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

y^'=(y+2t)^2,y(0)=sqrt(3)

y^{^{'}} = (y + 2 t)^{2}, y (0) = 3

(\partial)/(\partial x)(x^7-6xy-3y^2)

\frac{\partial}{\partial x} (x^{7} - 6 x y - 3 y^{2})

integral of (sin(x/2)+cos(x/2))^2

\int (sin (\frac{x}{2}) + cos (\frac{x}{2}))^{2} d x

Frequently Asked Questions (FAQ)

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