derivative of (sin(x)^{x^3})

Lösung

\frac{d}{d x} ((sin (x))^{x^{3}})

sin^{x^{3}} (x) (3 x^{2} ln (sin (x)) + x^{3} cot (x))

Schritte zur Lösung

\frac{d}{d x} ((sin (x))^{x^{3}})

Wende Exponentenregel an:

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

(sin (x))^{x^{3}} = e^{x^{3} l n (s i n (x))}

= \frac{d}{d x} (e^{x^{3} l n (s i n (x))})

Wende die Kettenregel an:

e^{x^{3} l n (s i n (x))} \frac{d}{d x} (x^{3} ln (sin (x)))

= e^{x^{3} l n (s i n (x))} \frac{d}{d x} (x^{3} ln (sin (x)))

\frac{d}{d x} (x^{3} ln (sin (x))) = 3 x^{2} ln (sin (x)) + cot (x) x^{3}

= e^{x^{3} l n (s i n (x))} (3 x^{2} ln (sin (x)) + cot (x) x^{3})

e^{x^{3} l n (s i n (x))} = sin^{x^{3}} (x)

= sin^{x^{3}} (x) (3 x^{2} ln (sin (x)) + x^{3} cot (x))

d er i v a t i v e y = ln (9 x)

x \to \infty lim (m x + b)

\int \frac{1}{( x ^{2} - 8 x ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial x} (\frac{( 5 x + 3 )}{y - 2})

\int 20