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)

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derivative of

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

\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}}

\frac{1 - 1}{x}

3 ln (6 x + 1)

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

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

\frac{q}{2}

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)