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Beliebt Vorkalkül >

derivative y=(cos(x))^x

Lösung

ableitung von

y = (cos (x))^{x}

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

Graph

Beliebte Beispiele

p o l a r (3, - 2)

derivative 3e^x

d er i v a t i v e 3 e^{x}

ma g ni t u d e (2 - 1)

derivative f(x)=3-4x^2

d er i v a t i v e f (x) = 3 - 4 x^{2}

p o l a r (2, 0)