(\partial)/(\partial x)((xz)/(x^2+y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int cos (3 x) (2 + sin (3 x))^{4} d x

\frac{d}{d a} (sin (a) + sin (2 a))

\frac{d}{d x} (\frac{23}{x ^{4}})

\int \frac{1}{tan ( 5 θ )} d θ

f (x) = x^{\frac{1}{2}}