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Beliebt Rechnen >

derivative of a^xln(x)

Lösung

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

Lösung

a^{x} ln (a) ln (x) + \frac{a ^{x}}{x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = a^{x}, g = ln (x)

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= a^{x} ln (a) ln (x) + \frac{1}{x} a^{x}

\frac{1}{x} a^{x} = \frac{a ^{x}}{x}

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

Graph

Beliebte Beispiele

11x-4ysqrt(x^2+1)(dy)/(dx)=0

11 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

derivative f(t)=sqrt(4t^2-t)

d er i v a t i v e f (t) = 4 t^{2} - t

limit as x approaches 1 of x^2-x

x \to 1 lim (x^{2} - x)

tangent 9x^2-x^3

t an g e n t 9 x^{2} - x^{3}

derivative of 2(pi-e^4)

\frac{d}{d x} (2 (π - e)^{4})