derivative f(x)=x^{cos(x)}

Lösung

ableitung von

f (x) = x^{c o s (x)}

x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{c o s (x)})

Wende Exponentenregel an:

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

x^{c o s (x)} = e^{c o s (x) l n (x)}

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

Wende die Kettenregel an:

e^{c o s (x) l n (x)} \frac{d}{d x} (cos (x) ln (x))

= e^{c o s (x) l n (x)} \frac{d}{d x} (cos (x) ln (x))

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

= e^{c o s (x) l n (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{c o s (x) l n (x)} = x^{c o s (x)}

= x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})