derivative of (cos(6x)^x)

Lösung

\frac{d}{d x} ((cos (6 x))^{x})

cos^{x} (6 x) (ln (cos (6 x)) - 6 x tan (6 x))

Schritte zur Lösung

\frac{d}{d x} ((cos (6 x))^{x})

Wende Exponentenregel an:

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

(cos (6 x))^{x} = e^{x l n (c o s (6 x))}

= \frac{d}{d x} (e^{x l n (c o s (6 x))})

Wende die Kettenregel an:

e^{x l n (c o s (6 x))} \frac{d}{d x} (x ln (cos (6 x)))

= e^{x l n (c o s (6 x))} \frac{d}{d x} (x ln (cos (6 x)))

\frac{d}{d x} (x ln (cos (6 x))) = ln (cos (6 x)) - 6 x tan (6 x)

= e^{x l n (c o s (6 x))} (ln (cos (6 x)) - 6 x tan (6 x))

e^{x l n (c o s (6 x))} = cos^{x} (6 x)

= cos^{x} (6 x) (ln (cos (6 x)) - 6 x tan (6 x))

x \to 0 lim (x^{3} ln (x))

x \to 0 lim (\frac{1 - 6 x}{x})

\int \frac{x}{( x + 1 )} d x

\int \frac{6}{x ^{2} + 1} d x

\int \frac{sin ( x )}{1 - cos ( x )} d x