derivative (sin(x))^x

Lösung

ableitung von

(sin (x))^{x}

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

Schritte zur Lösung

\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))}

= \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)

= 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)

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

t an g e n t x^{3} - 2 x + 2 (4.58)

\frac{\partial}{\partial x} (3 x - 7 y)

y^{^{'}} cos (x) + y sin (x) = 2 cos^{3} (x) sin (x)

h \to 0 lim (\frac{2 ^{- h} - 1}{h})

d er i v a t i v e arcsin (\frac{x}{3}) + C