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Popular >

derivative of x/(x^2+a^2)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

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

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

Graph

Popular Examples

integral of (x+3)^{1/2}

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

(dy)/(dx)7x^3+7y^3-5xy=0

\frac{d y}{d x} 7 x^{3} + 7 y^{3} - 5 x y = 0

integral of 1/(x(5+9ln(x)))

\int \frac{1}{x ( 5 + 9 ln ( x ) )} d x

limit as x approaches 0 of (1-7x)^{5/x}

x \to 0 lim ((1 - 7 x)^{\frac{5}{x}})

derivative of g(x)=(ln(x))/(x^2)derivative of

g (x) = \frac{ln ( x )}{x ^{2}}

Frequently Asked Questions (FAQ)

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