derivative of (cos^2(x)^x)

Lösung

\frac{d}{d x} ((cos^{2} (x))^{x})

cos^{2 x} (x) (ln (cos^{2} (x)) - 2 x tan (x))

Schritte zur Lösung

\frac{d}{d x} ((cos^{2} (x))^{x})

Wende Exponentenregel an:

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

(cos^{2} (x))^{x} = e^{x l n (c o s^{2} (x))}

= \frac{d}{d x} (e^{x l n (c o s^{2} (x))})

Wende die Kettenregel an:

e^{x l n (c o s^{2} (x))} \frac{d}{d x} (x ln (cos^{2} (x)))

= e^{x l n (c o s^{2} (x))} \frac{d}{d x} (x ln (cos^{2} (x)))

\frac{d}{d x} (x ln (cos^{2} (x))) = ln (cos^{2} (x)) - 2 x tan (x)

= e^{x l n (c o s^{2} (x))} (ln (cos^{2} (x)) - 2 x tan (x))

e^{x l n (c o s^{2} (x))} = cos^{2 x} (x)

= cos^{2 x} (x) (ln (cos^{2} (x)) - 2 x tan (x))