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}})

Simplify

\frac{- x}{y ^{2} + x ^{2}} : - \frac{x}{y ^{2} + x ^{2}}

= \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}}

\int t^{5} ln (t) d t

d er i v a t i v e e^{(e^{(x)} - x)}

t an g e n t f (x) = 2 x^{2} + 3 x, (- 3, 9)

\frac{d}{d x} ((x^{3} - 1)^{4})

\frac{\partial}{\partial x} (11 - 4 x^{2} - y^{2})

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)