derivative of x^pe^{ax}

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x^{p}) = x^{p} (ln (x) \frac{d p}{d x} + \frac{p}{x})

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

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

\int \frac{y}{1 - y ^{2}} d y

\frac{\partial}{\partial x} (- 1 + ln (x))

\int \frac{1}{4 8 - 3 x} d x

d er i v a t i v e \frac{4 x + x ^{2} - 2}{( 2 + x ) ^{2}}

\frac{d}{d x} (\frac{3 x ^{2} - 5}{2 x ^{2} + 1})