(\partial)/(\partial x)(x/(x+3y))

Lösung

\frac{\partial}{\partial x} (\frac{x}{x + 3 y})

\frac{3 y}{( x + 3 y ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{x + 3 y})

Behandle

y

als Konstante

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial x} ( x ) ( x + 3 y ) - \frac{\partial}{\partial x} ( x + 3 y ) x}{( x + 3 y ) ^{2}}

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

\frac{\partial}{\partial x} (x + 3 y) = 1

= \frac{1 \cdot ( x + 3 y ) - 1 \cdot x}{( x + 3 y ) ^{2}}

1 \cdot (x + 3 y) - 1 \cdot x = 3 y

= \frac{3 y}{( x + 3 y ) ^{2}}

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

\int 28 x^{3} - 18 x^{2} + 8 x d x

(cos (x))^{^{'}}

x \to 3 lim ([3 (8) (- 10)])

\frac{d}{d x} (e^{x y}) = \frac{d}{d x} (2 y)