derivative of 3x^{4x}

Lösung

\frac{d}{d x} (3 x^{4 x})

12 x^{4 x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (3 x^{4 x})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

x^{4 x} = e^{4 x l n (x)}

= 3 \frac{d}{d x} (e^{4 x l n (x)})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (4 x ln (x)) = 4 (ln (x) + 1)

= 3 e^{4 x l n (x)} \cdot 4 (ln (x) + 1)

Vereinfache

3 e^{4 x l n (x)} \cdot 4 (ln (x) + 1) : 12 x^{4 x} (ln (x) + 1)

= 12 x^{4 x} (ln (x) + 1)

\frac{\partial}{\partial x} (x \cdot \frac{e ^{y}}{x + y})

n = 8 \sum \infty \frac{n}{n ln ( n )}

\frac{\partial}{\partial x} (ln (x + 8 y + 9 z))

d er i v a t i v e f (x) = \frac{( x ^{2} - 1 )}{( x ^{2} + x + 1 )}

x \to 1 - lim (\frac{x}{x + 1})