derivative of 3^{sin(x})

Lösung

\frac{d}{d x} (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)

\frac{d}{d x} (tan (5 x))

x \to 1 lim (3 x^{3} - 5 x^{2} + 5)

\int \frac{x ^{2}}{4 x ^{2} + 1} d x

d er i v a t i v e 7 e^{1 - x^{2}}

\int (\frac{1 + x}{x})^{3} d x