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Beliebt Rechnen >

derivative of (cos(2x)^x)

Lösung

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

Lösung

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

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

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

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

Graph

Beliebte Beispiele

integral from 1 to infinity of 2e^{-2x}

\int_{1}^{\infty} 2 e^{- 2 x} d x

integral of (x^2)arcsin(x)

\int (x^{2}) arcsin (x) d x

integral of (2y^2)

\int (2 y^{2}) d y

integral of r/(sqrt(a^2-r^2))

\int \frac{r}{a ^{2} - r ^{2}} d r

integral from-1 to 2 of x(1+x^3)

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