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

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

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

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

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

Solution steps

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

Simplify

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

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

Treat

c, y

as a constant

Take the constant out:

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

= - c \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}}

= - c \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

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

Simplify

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

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

\frac{k ^{4}}{( s + k ) ^{5}}

\frac{\partial}{\partial x} (\frac{( y ^{4} )}{x})

2 y^{^{'}} - y = 0

x \to 0 lim (5 x - 12)

\int x arctan (d) x d x

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