de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative 3^{(x^5)}

Lösung

ableitung von

3^{(x^{5})}

Lösung

5 ln (3) \cdot 3^{x^{5}} x^{4}

Schritte zur Lösung

\frac{d}{d x} (3^{x^{5}})

Wende Exponentenregel an:

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

3^{x^{5}} = e^{x^{5} l n (3)}

= \frac{d}{d x} (e^{x^{5} l n (3)})

Wende die Kettenregel an:

e^{x^{5} l n (3)} \frac{d}{d x} (x^{5} ln (3))

= e^{x^{5} l n (3)} \frac{d}{d x} (x^{5} ln (3))

\frac{d}{d x} (x^{5} ln (3)) = 5 ln (3) x^{4}

= e^{x^{5} l n (3)} \cdot 5 ln (3) x^{4}

e^{x^{5} l n (3)} = 3^{x^{5}}

= 5 ln (3) \cdot 3^{x^{5}} x^{4}

Graph

Beliebte Beispiele

sum from n=0 to infinity of sqrt(1+n)

n = 0 \sum \infty 1 + n

y^'+2y=4,y(0)=4

y^{^{'}} + 2 y = 4, y (0) = 4

derivative of 1/2 tan(x)

\frac{d}{d x} (\frac{1}{2} tan (x))

integral from 6 to 8 of (50)/((x-6)^3)

\int_{6}^{8} \frac{50}{( x - 6 ) ^{3}} d x

integral of sqrt((6+x)/(6-x))

\int \frac{6 + x}{6 - x} d x