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Beliebt Rechnen >

derivative of (cos(x)^x)

Lösung

\frac{d}{d x} ((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

tangent ((x-1))/(x+1)

t an g e n t \frac{( x - 1 )}{x + 1}

tangent-7x^4+11x^2-4

t an g e n t - 7 x^{4} + 11 x^{2} - 4

integral of (x^2)/((1+9x^2)^{3/2)}

\int \frac{x ^{2}}{( 1 + 9 x ^{2} ) ^{\frac{3}{2}}} d x

limit as x approaches 6 of (x-2)^2

x \to 6 lim ((x - 2)^{2})

4((dy)/(dx))-(y)-x=0

4 (\frac{d y}{d x}) - (y) - x = 0