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Beliebt Rechnen >

derivative of xe^{xa}

Lösung

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

Lösung

e^{a x} + a e^{a x} x

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = e^{x a}

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

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

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

= 1 \cdot e^{x a} + e^{x a} a x

Vereinfache

= e^{a x} + a e^{a x} x

Graph

Beliebte Beispiele

limit as x approaches infinity of-1^xx

x \to \infty lim (- 1^{x} x)

derivative of 4sin^5(sqrt(x))

\frac{d}{d x} (4 sin^{5} (x))

integral of (1+1/(2x))

\int (1 + \frac{1}{2 x}) d x

tangent x/(1+x^2)

t an g e n t \frac{x}{1 + x ^{2}}

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

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