de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of 3x^{3x}

Lösung

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

Lösung

9 x^{3 x} (ln (x) + 1)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

= 3 e^{3 x l n (x)} \cdot 3 (ln (x) + 1)

Vereinfache

3 e^{3 x l n (x)} \cdot 3 (ln (x) + 1) : 9 x^{3 x} (ln (x) + 1)

= 9 x^{3 x} (ln (x) + 1)

Graph

Beliebte Beispiele

derivative of 5-2sin(x-e^x)

\frac{d}{d x} (5 - 2 sin (x) - e^{x})

integral of t/((3t^2+1)^4)

\int \frac{t}{( 3 t ^{2} + 1 ) ^{4}} d t

y^'+y=cos(t),y(0)=1

y^{^{'}} + y = cos (t), y (0) = 1

derivative y=log_{e}(log_{e}(x))

d er i v a t i v e y = lo g_{e} (lo g_{e} (x))

limit as h approaches 0 of ((h+2)^3-8)/h

h \to 0 lim (\frac{( h + 2 ) ^{3} - 8}{h})