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Beliebt Rechnen >

derivative of (4x^x)

Lösung

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

Lösung

(ln (4 x) + 1) (4 x)^{x}

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

(4 x)^{x} = e^{x l n (4 x)}

= \frac{d}{d x} (e^{x l n (4 x)})

Wende die Kettenregel an:

e^{x l n (4 x)} \frac{d}{d x} (x ln (4 x))

= e^{x l n (4 x)} \frac{d}{d x} (x ln (4 x))

\frac{d}{d x} (x ln (4 x)) = ln (4 x) + 1

= e^{x l n (4 x)} (ln (4 x) + 1)

e^{x l n (4 x)} = (4 x)^{x}

= (ln (4 x) + 1) (4 x)^{x}

Graph

Beliebte Beispiele

integral of 10x^4-2sec^2(x)

\int 10 x^{4} - 2 sec^{2} (x) d x

tangent 4/(x^2)

t an g e n t \frac{4}{x ^{2}}

t an g e n t \frac{9}{x}

steigung x^2+xy-(y^2)/4 =1

s l o p e x^{2} + x y - \frac{y ^{2}}{4} = 1

derivative f(x)=(5x+2x^2)^2

d er i v a t i v e f (x) = (5 x + 2 x^{2})^{2}