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Popular >

derivative of (-3+x^2^{-1})

Solution

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

Solution

- \frac{2 x}{( - 3 + x ^{2} ) ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{2 x}{( - 3 + x ^{2} ) ^{2}}

Popular Examples

inverse oflaplace ((1+e^{-2s})^2)/(s+2)inverse laplace

\frac{( 1 + e ^{- 2 s} ) ^{2}}{s + 2}

derivative of sin(x^2+3)

\frac{d}{d x} (sin (x^{2} + 3))

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\int_{- 1}^{1} x + 1 d x

limit as n approaches infinity of (1+\sqrt[3]{n})/(1+\sqrt[3]{n+1)}

\frac{d x}{d t} = e^{t}

Frequently Asked Questions (FAQ)

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