derivative (sin(3x))^{ln(x)}

Lösung

ableitung von

(sin (3 x))^{l n (x)}

x^{l n (s i n (3 x))} (\frac{ln ( sin ( 3 x ) )}{x} + 3 cot (3 x) ln (x))

Schritte zur Lösung

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

Wende Exponentenregel an:

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

(sin (3 x))^{l n (x)} = e^{l n (x) l n (s i n (3 x))}

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

Wende die Kettenregel an:

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

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

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

= e^{l n (x) l n (s i n (3 x))} (\frac{ln ( sin ( 3 x ) )}{x} + 3 cot (3 x) ln (x))

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

= x^{l n (s i n (3 x))} (\frac{ln ( sin ( 3 x ) )}{x} + 3 cot (3 x) ln (x))

\frac{\partial}{\partial x} (2 x + y^{2})

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n = 0 \sum \infty 4 (\frac{2}{3})^{2 n}

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