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

Lösung

\frac{d}{d x} (cos^{s i n (x)} (x))

cos^{s i n (x)} (x) (cos (x) ln (cos (x)) - tan (x) sin (x))

Schritte zur Lösung

\frac{d}{d x} (cos^{s i n (x)} (x))

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

= cos^{s i n (x)} (x) (cos (x) ln (cos (x)) - tan (x) sin (x))

\frac{d}{d x} (sin (x^{2} + 3 x))

\frac{\partial}{\partial x} (\frac{2 x - 3 y}{2 x + 3 y})

\int \frac{arcsin ( 6 x )}{1 - 36 x ^{2}} d x

d er i v a t i v e y = x^{\frac{1}{x}}

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y ^{2} + z ^{2}})