(\partial)/(\partial y)((x+y)e^{y^2})

Lösung

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

e^{y^{2}} + 2 e^{y^{2}} y (x + y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + y, g = e^{y^{2}}

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

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

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

= 1 \cdot e^{y^{2}} + e^{y^{2}} \cdot 2 y (x + y)

Vereinfache

= e^{y^{2}} + 2 e^{y^{2}} y (x + y)

l a pl a ce t r an s f or m 3 t + 4

d er i v a t i v e f (x) = x^{3} + x^{2} + x + 1

\int e^{x} cos (e^{x}) d x

a re a y = e^{3 x}, y = e^{x}, [0, 1]

\int_{0}^{9} \frac{x}{( x + 9 ) ^{4}} d x