de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative f(x)=4x^{5x}

Lösung

ableitung von

f (x) = 4 x^{5 x}

Lösung

20 x^{5 x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (4 x^{5 x})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

= 4 \frac{d}{d x} (e^{5 x l n (x)})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (5 x ln (x)) = 5 (ln (x) + 1)

= 4 e^{5 x l n (x)} \cdot 5 (ln (x) + 1)

Vereinfache

4 e^{5 x l n (x)} \cdot 5 (ln (x) + 1) : 20 x^{5 x} (ln (x) + 1)

= 20 x^{5 x} (ln (x) + 1)

Graph

Beliebte Beispiele

y^'+ycos(x)=2cos(x),y(0)=4

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

integral of x^3e^{2x^2}

\int x^{3} e^{2 x^{2}} d x

derivative of e^{sin(x+cos(x)})

\frac{d}{d x} (e^{s i n (x) + c o s (x)})

derivative of sqrt((sin(20x)^3))

\frac{d}{d x} ((sin (20 x))^{3})

tangent sqrt(x+3)

t an g e n t x + 3