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Beliebt Rechnen >

(\partial)/(\partial y)(ye^y)

Lösung

\frac{\partial}{\partial y} (y e^{y})

Lösung

e^{y} + e^{y} y

Schritte zur Lösung

\frac{\partial}{\partial y} (y e^{y})

Wende die Produktregel an:

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

f = y, g = e^{y}

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

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

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

= 1 \cdot e^{y} + e^{y} y

Vereinfache

= e^{y} + e^{y} y

Beliebte Beispiele

integral of e^{5x}sin(3x)

\int e^{5 x} sin (3 x) d x

tangent x^3+y^3=6xy,(3,3)

t an g e n t x^{3} + y^{3} = 6 x y, (3, 3)

derivative x-x^3

d er i v a t i v e x - x^{3}

integral of (3e^{2x})/(e^{2x)+15e^x+54}

\int \frac{3 e ^{2 x}}{e ^{2 x} + 15 e ^{x} + 54} d x

f (x) = \frac{4}{x ^{2}}