derivative y=sqrt(x)^{3x}

Lösung

ableitung von

y = x^{3 x}

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

Schritte zur Lösung

\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)}

= \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) + \frac{1}{2})

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

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

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

y^{^{''}} + y = sec (t)

n = 1 \sum \infty \frac{6 n}{9 - 2 n}

ma c l a u r in f (x) = (1 + x)^{- \frac{5}{3}}

\int x^{2} (6 x^{3} - 5)^{4} d x

x \to 0 lim (\frac{3 ^{x}}{3 ^{x} - 1})