derivative 9(sin(x))^x

Lösung

ableitung von

9 (sin (x))^{x}

9 sin^{x} (x) (ln (sin (x)) + x cot (x))

Schritte zur Lösung

\frac{d}{d x} (9 (sin (x))^{x})

Entferne die Konstante:

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

= 9 \frac{d}{d x} ((sin (x))^{x})

Wende Exponentenregel an:

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

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

= 9 \frac{d}{d x} (e^{x l n (s i n (x))})

Wende die Kettenregel an:

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

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

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

= 9 e^{x l n (s i n (x))} (ln (sin (x)) + x cot (x))

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

= 9 sin^{x} (x) (ln (sin (x)) + x cot (x))

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