What is the derivative of x/((x^2+y^2)) ?

The derivative of x/((x^2+y^2)) is (-x^2+y^2)/((x^2+y^2)^2)

What is the first derivative of x/((x^2+y^2)) ?

The first derivative of x/((x^2+y^2)) is (-x^2+y^2)/((x^2+y^2)^2)

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derivative of

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

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

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

x^{3} - 3 x^{2} - 20

(3 x + 1)^{3}

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

y = (x^{- 2}) ln (x)

\frac{d}{d t} (4 cos^{3} (t))

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