(\partial)/(\partial y)(x^2+y^2+z^2+xy)

Lösung

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

x + 2 y

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

\frac{\partial}{\partial y} (z^{2}) = 0

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

= 0 + 2 y + 0 + x

Vereinfache

= x + 2 y

l a pl a ce t r an s f or m e^{- 3 t} sin (4 t)

d er i v a t i v e f (x) = 6 3 x

\int \frac{25 - 4 x ^{2}}{x} d x

\int cot^{3} (3 x) csc^{5} (3 x) d x

\frac{d}{d x} (4 \frac{e ^{5 x}}{x ^{2} + 1})