(\partial)/(\partial x)((x+y)/(x*y))

Lösung

\frac{\partial}{\partial x} (\frac{x + y}{x \cdot y})

- \frac{1}{x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x + y}{x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= - \frac{1}{x ^{2}}

\frac{d}{d x} (lo g_{3} (4 x))

\frac{d}{d θ} (\frac{8}{2 + cot ( θ ) sin ( θ )})

\int \frac{1}{x ( ln ( x ) ) ^{4}} d x

d er i v a t i v e y = (7 x + 3) x^{2}

t a y l or cos (x) (\frac{π}{2})