(\partial)/(\partial y)(1/2 (x-y)^2)

Lösung

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

- x + y

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

2 (x - y) \frac{\partial}{\partial y} (x - y)

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

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

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

Vereinfache

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

= - x + y

x \to 2 lim (x^{2} - 4 x + 2)

in v erse l a pl a ce \frac{1}{2 s ^{2} + s}

\int \frac{1}{x ^{1}} d x

\int \frac{sin ( 1 + x )}{x} d x

\int_{x}^{5} sin (t^{3}) d t