derivative of 3^{cos(2x})

Lösung

\frac{d}{d x} (3^{c o s (2 x)})

- 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

Schritte zur Lösung

\frac{d}{d x} (3^{c o s (2 x)})

Wende Exponentenregel an:

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

3^{c o s (2 x)} = e^{c o s (2 x) l n (3)}

= \frac{d}{d x} (e^{c o s (2 x) l n (3)})

Wende die Kettenregel an:

e^{c o s (2 x) l n (3)} \frac{d}{d x} (cos (2 x) ln (3))

= e^{c o s (2 x) l n (3)} \frac{d}{d x} (cos (2 x) ln (3))

\frac{d}{d x} (cos (2 x) ln (3)) = - 2 ln (3) sin (2 x)

= e^{c o s (2 x) l n (3)} (- 2 ln (3) sin (2 x))

Vereinfache

e^{c o s (2 x) l n (3)} (- 2 ln (3) sin (2 x)) : - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

= - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

x \to 3 lim (\frac{10}{x ^{2}})

\int_{0}^{4} (\frac{5 x}{x ^{2} + 9}) d x

\frac{d}{d x} ((2 x + x) (x^{2} - x))

d er i v a t i v e sec^{2} (θ)

\frac{d}{d x} (\frac{cos ( x )}{x ^{6}})