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Popular >

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

Solution

derivative of

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

Solution

- \frac{2}{x ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{2}{x ^{3}}

Popular Examples

derivative of 1/((x^2-1(x^2+x+1)))

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

integral of 1/(x(10-x))

\int \frac{1}{x ( 10 - x )} d x

(\partial)/(\partial x)((x+2)/(y+1))

\frac{\partial}{\partial x} (\frac{x + 2}{y + 1})

derivative of xe^{9x}

\frac{d}{d x} (x e^{9 x})

derivative of 3/4 x^{4/3}-3/8 x^{2/3}+9

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 9)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2)^{-1} ?
The derivative of (x^2)^{-1} is -2/(x^3)
What is the first derivative of (x^2)^{-1} ?
The first derivative of (x^2)^{-1} is -2/(x^3)