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Beliebt Rechnen >

derivative (2x)^x

Lösung

ableitung von

(2 x)^{x}

Lösung

(ln (2 x) + 1) (2 x)^{x}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

(2 x)^{x} = e^{x l n (2 x)}

= \frac{d}{d x} (e^{x l n (2 x)})

Wende die Kettenregel an:

e^{x l n (2 x)} \frac{d}{d x} (x ln (2 x))

= e^{x l n (2 x)} \frac{d}{d x} (x ln (2 x))

\frac{d}{d x} (x ln (2 x)) = ln (2 x) + 1

= e^{x l n (2 x)} (ln (2 x) + 1)

e^{x l n (2 x)} = (2 x)^{x}

= (ln (2 x) + 1) (2 x)^{x}

Graph

Beliebte Beispiele

integral of 2/(16+3x^2)

\int \frac{2}{16 + 3 x ^{2}} d x

derivative regardsp I/(2p)

d er i v a t i v e re g a r d s p \frac{I}{2 p}

integral of 1/(4(1-x)^2)

\int \frac{1}{4 ( 1 - x ) ^{2}} d x

(d^2y)/(dx^2)=4x

\frac{d ^{2} y}{d x ^{2}} = 4 x

integral of (6x^2+x+6)/((x^2+1)^2)

\int \frac{6 x ^{2} + x + 6}{( x ^{2} + 1 ) ^{2}} d x