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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{x ^{c o s (x)}} \frac{d}{d x} (x^{c o s (x)})

= \frac{1}{x ^{c o s (x)}} \frac{d}{d x} (x^{c o s (x)})

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

= \frac{1}{x ^{c o s (x)}} x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Vereinfache

\frac{1}{x ^{c o s (x)}} x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x}) : - sin (x) ln (x) + \frac{cos ( x )}{x}

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

Graph

Beliebte Beispiele

tangent xy+1+e=e^{-xy},(1,-1)

t an g e n t x y + 1 + e = e^{- x y}, (1, - 1)

integral of 6xy^2

\int 6 x y^{2} d y

tangent f(x)=e^x,\at x=ln(14)

t an g e n t f (x) = e^{x}, at x = ln (14)

limit as x approaches 2 of sqrt(2x-4)+8

x \to 2 lim (2 x - 4 + 8)

integral of (cot(x))

\int (cot (x)) d x