derivative of (-cx/(x^2+y^2))

Lösung

\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}}

Schritte zur Lösung

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

Vereinfache

\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}})

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\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}}

Vereinfache

- 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}}

t an g e n t y = x^{3} - 3 x + 1, (4, 53)

t an g e n t y = \frac{x}{x + 1}

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

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