What is (\partial)/(\partial x)(-x/((x^2+y^2))) ?

The answer to (\partial)/(\partial x)(-x/((x^2+y^2))) is -(-x^2+y^2)/((x^2+y^2)^2)

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(\partial)/(\partial x)(-x/((x^2+y^2)))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial 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}}

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x}

x \to 0 + lim ((ln (x))^{2})

sec^{2} (x) + tan^{2} (x)

f (x) = 15 x - 1.86 x^{2}, at x = a

\frac{d}{d x} (7^{x^{2}})

What is (\partial)/(\partial x)(-x/((x^2+y^2))) ?
The answer to (\partial)/(\partial x)(-x/((x^2+y^2))) is -(-x^2+y^2)/((x^2+y^2)^2)