derivative 3^{sin(x)}

Lösung

ableitung von

3^{s i n (x)}

ln (3) \cdot 3^{s i n (x)} cos (x)

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

= ln (3) \cdot 3^{s i n (x)} cos (x)

\int \frac{1}{8} e^{8 x} d x

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\frac{d y}{d x} - \frac{2 y}{x} = x^{2} sin (3 x)