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Popular >

derivative of 1/(2+x^2)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

t^2y^{''}+11ty^'+25y=0,y(1)=4,y^'(1)=9

t^{2} y^{^{''}} + 11 t y^{^{'}} + 25 y = 0, y (1) = 4, y^{^{'}} (1) = 9

integral of 18-(54)/(15-2x)

\int 18 - \frac{54}{15 - 2 x} d x

derivative of ((x^2-4^2)/((x^2+2)^3))

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

integral of 1/(sqrt(y-1))

\int \frac{1}{y - 1} d y

limit as x approaches 1 of 1^2-3

x \to 1 lim (1^{2} - 3)

Frequently Asked Questions (FAQ)

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