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

The derivative of (-cx/(x^2+y^2)) is -(c(-x^2-2xy\frac{dy)/(dx)+y^2)}{(x^2+y^2)^2}

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

The first derivative of (-cx/(x^2+y^2)) is -(c(-x^2-2xy\frac{dy)/(dx)+y^2)}{(x^2+y^2)^2}

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

= - c \frac{d}{d 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{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 + 2 y \frac{d y}{d x}

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

Simplify

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

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

n = 0 \sum \infty \frac{1}{4 + e ^{- n}}

y = x^{3} - 3 x + 1, (4, 53)

y = \frac{x}{x + 1}

y^{^{'''}} + 5 y^{^{''}} = 0

\int_{0}^{1} (x - x^{2}) d x

What is the derivative of (-cx/(x^2+y^2)) ?
The derivative of (-cx/(x^2+y^2)) is -(c(-x^2-2xy\frac{dy)/(dx)+y^2)}{(x^2+y^2)^2}
What is the first derivative of (-cx/(x^2+y^2)) ?
The first derivative of (-cx/(x^2+y^2)) is -(c(-x^2-2xy\frac{dy)/(dx)+y^2)}{(x^2+y^2)^2}