derivative of sin^x(x)

Lösung

\frac{d}{d x} (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 \frac{x ^{3} + 1}{2 x}

x \to 8 lim (\frac{x + 6}{x - 8})

\int 16 x e^{- x^{2}} d x

x \to - 2 lim (- x^{2} + 6 x - 5)

\int (x - 7)^{5} d x