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Beliebt Rechnen >

derivative x^{cos(x)}

Lösung

ableitung von

x^{c o s (x)}

Lösung

x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{c o s (x)})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

= x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Graph

Beliebte Beispiele

-5t^2y^{''}+ty^'+8y=0

- 5 t^{2} y^{^{''}} + t y^{^{'}} + 8 y = 0

fläche 3/x ,12x, 1/3 x

a re a \frac{3}{x}, 12 x, \frac{1}{3} x

integral of rsqrt(1+4r^2)

\int r 1 + 4 r^{2} d r

tangent f(x)=cos(x),\at x= pi/4

t an g e n t f (x) = cos (x), at x = \frac{π}{4}

derivative x5^x

d er i v a t i v e x 5^{x}