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Beliebt Rechnen >

derivative of x*e^y

Lösung

\frac{d}{d x} (x \cdot e^{y})

Lösung

e^{y} + e^{y} x \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (x e^{y})

Wende die Produktregel an:

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

f = x, g = e^{y}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{y}) = e^{y} \frac{d y}{d x}

= 1 \cdot e^{y} + e^{y} \frac{d y}{d x} x

Vereinfache

= e^{y} + e^{y} x \frac{d y}{d x}

Beliebte Beispiele

integral of ((x+2))/(x^2+4)

\int \frac{( x + 2 )}{x ^{2} + 4} d x

-4x^2y+y^'=-10x^2

- 4 x^{2} y + y^{^{'}} = - 10 x^{2}

f (x) = \frac{e ^{x}}{x}

d er i v a t i v e 8 t

(d^2)/(dx^2)(sqrt(x+7))

\frac{d ^{2}}{d x ^{2}} (x + 7)