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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Quotientenregel an:

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

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

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

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

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

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

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

\int_{- 2}^{3} \frac{31}{x ^{4}} d x

\frac{d}{d x} (10)

a re a 4 x, 4, \frac{4}{x}, 0

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

\int \frac{1}{13 x - 2 x ^{2} - 15} d x