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Popular >

derivative of 1/(x^2+c)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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

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

limit as x approaches 0+of xe^{-2/x}

x \to 0 + lim (x e^{- \frac{2}{x}})

y^'+2ty=e^{-t^2}

y^{^{'}} + 2 t y = e^{- t^{2}}

integral from 0 to pi of 6cos^2(3x)

\int_{0}^{π} 6 cos^{2} (3 x) d x

integral of (x^2-4x+5)^2

\int (x^{2} - 4 x + 5)^{2} d x

Frequently Asked Questions (FAQ)

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