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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

\frac{d}{d x} (2 e^{- 2 x} x - 2 e^{- 2 x} x^{2})

(4 - x^{2})^{^{'}}

\frac{d}{d x} (sin (x) e^{- c o s (x)})

x \to 100000 lim (x^{3} + 2 x + 1)

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

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