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Beliebt Rechnen >

derivative of x^{ln(3x})

Lösung

\frac{d}{d x} (x^{l n (3 x)})

Lösung

3^{l n (x)} x^{l n (x) - 1} ln (3 x^{2})

Schritte zur Lösung

\frac{d}{d x} (x^{l n (3 x)})

Wende Exponentenregel an:

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

x^{l n (3 x)} = e^{l n (3 x) l n (x)}

= \frac{d}{d x} (e^{l n (3 x) l n (x)})

Wende die Kettenregel an:

e^{l n (3 x) l n (x)} \frac{d}{d x} (ln (3 x) ln (x))

= e^{l n (3 x) l n (x)} \frac{d}{d x} (ln (3 x) ln (x))

\frac{d}{d x} (ln (3 x) ln (x)) = \frac{ln ( 3 x ^{2} )}{x}

= e^{l n (3 x) l n (x)} \frac{ln ( 3 x ^{2} )}{x}

Vereinfache

e^{l n (3 x) l n (x)} \frac{ln ( 3 x ^{2} )}{x} : 3^{l n (x)} x^{l n (x) - 1} ln (3 x^{2})

= 3^{l n (x)} x^{l n (x) - 1} ln (3 x^{2})

Graph

Beliebte Beispiele

integral of 1/(sqrt(529+x^2))

\int \frac{1}{529 + x ^{2}} d x

derivative of 9ln(x)

\frac{d}{d x} (9 ln (x))

derivative 11e^x

d er i v a t i v e 11 e^{x}

integral from 0 to 5 of sqrt(5x)

\int_{0}^{5} 5 x d x

derivative (1-5t)/(4+t)

d er i v a t i v e \frac{1 - 5 t}{4 + t}