de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of 3^{sqrt(x^3-x+1)}

Lösung

\frac{d}{d x} (3^{x^{3} - x + 1})

Lösung

\frac{ln ( 3 ) \cdot 3 ^{x^{3} - x + 1} ( 3 x ^{2} - 1 )}{2 x ^{3} - x + 1}

Schritte zur Lösung

\frac{d}{d x} (3^{x^{3} - x + 1})

Wende Exponentenregel an:

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

3^{x^{3} - x + 1} = e^{x^{3} - x + 1 l n (3)}

= \frac{d}{d x} (e^{x^{3} - x + 1 l n (3)})

Wende die Kettenregel an:

e^{x^{3} - x + 1 l n (3)} \frac{d}{d x} (x^{3} - x + 1 ln (3))

= e^{x^{3} - x + 1 l n (3)} \frac{d}{d x} (x^{3} - x + 1 ln (3))

\frac{d}{d x} (x^{3} - x + 1 ln (3)) = \frac{ln ( 3 ) ( 3 x ^{2} - 1 )}{2 x ^{3} - x + 1}

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

Vereinfache

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

= \frac{ln ( 3 ) \cdot 3 ^{x^{3} - x + 1} ( 3 x ^{2} - 1 )}{2 x ^{3} - x + 1}

Graph

Beliebte Beispiele

derivative of arcsec(x/a)

\frac{d}{d x} (arcsec (\frac{x}{a}))

integral from-infinity to 0 of 1/(5-8x)

\int_{- \infty}^{0} \frac{1}{5 - 8 x} d x

derivative of x^2sec(1/(x^3))

\frac{d}{d x} (x^{2} sec (\frac{1}{x ^{3}}))

integral of (x^3)/(x^8+5)

\int \frac{x ^{3}}{x ^{8} + 5} d x

(\partial)/(\partial x)(e^{2y}(3e^y-2x))

\frac{\partial}{\partial x} (e^{2 y} (3 e^{y} - 2 x))