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

Lösung

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

\frac{6 y}{( x + 3 y ) ^{2}}

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{1 \cdot ( x + 3 y ) - 1 \cdot ( x - 3 y )}{( x + 3 y ) ^{2}} : \frac{6 y}{( x + 3 y ) ^{2}}

= \frac{6 y}{( x + 3 y ) ^{2}}

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x})

a re a y = x, 0, 1

d er i v a t i v e f (t) = e^{7 t \cdot s i n (2 t)}

x^{2} - 1, - x + 2, x = 0, x = 1

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