derivative of sin^{sin(x}(x))

Lösung

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

sin^{s i n (x)} (x) (cos (x) ln (sin (x)) + cos (x))

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

= sin^{s i n (x)} (x) (cos (x) ln (sin (x)) + cos (x))

f (x) = e^{x - 3}

f (x) = 2 x^{2} + x

f (x) = x^{2} - 7 x + 8

f (x) = 3 + 2 x

f (x) = 2 x^{3} + 3 x^{2} - 12 x - 7