derivative of (cos(x)^{ln(x)})

Lösung

\frac{d}{d x} ((cos (x))^{l n (x)})

x^{l n (c o s (x))} (\frac{ln ( cos ( x ) )}{x} - tan (x) ln (x))

Schritte zur Lösung

\frac{d}{d x} ((cos (x))^{l n (x)})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

d er i v a t i v e 2 + x

d er i v a t i v e \frac{1}{4 y ^{2}}

\int_{0}^{1} - 3 (x^{2} + 1) e^{- x} d x

\int 21 sin^{2} (x co) s^{2} x

\frac{\partial}{\partial x} (1 e^{1})