derivative 2^{sin(x)}

Lösung

ableitung von

2^{s i n (x)}

ln (2) \cdot 2^{s i n (x)} cos (x)

Schritte zur Lösung

\frac{d}{d x} (2^{s i n (x)})

Wende Exponentenregel an:

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

2^{s i n (x)} = e^{s i n (x) l n (2)}

= \frac{d}{d x} (e^{s i n (x) l n (2)})

Wende die Kettenregel an:

e^{s i n (x) l n (2)} \frac{d}{d x} (sin (x) ln (2))

= e^{s i n (x) l n (2)} \frac{d}{d x} (sin (x) ln (2))

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

= e^{s i n (x) l n (2)} ln (2) cos (x)

e^{s i n (x) l n (2)} = 2^{s i n (x)}

= ln (2) \cdot 2^{s i n (x)} cos (x)

\frac{d}{d x} (- \frac{200 ln ( \frac{x}{40} )}{x + 20})

\frac{d}{d x} (ln ((x + 1)^{2}))

\frac{\partial}{\partial x} (\frac{1}{x - a})

\int sin (x) sec^{2} (x) d x

\frac{\partial}{\partial x} (4 x^{3} + 4 x y^{2})