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Beliebt Rechnen >

derivative y=sin(ln(x))

Lösung

ableitung von

y = sin (ln (x))

Lösung

\frac{cos ( ln ( x ) )}{x}

Schritte zur Lösung

\frac{d}{d x} (sin (ln (x)))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= cos (ln (x)) \frac{1}{x}

Vereinfache

cos (ln (x)) \frac{1}{x} : \frac{cos ( ln ( x ) )}{x}

= \frac{cos ( ln ( x ) )}{x}

Graph

Beliebte Beispiele

(dx)/(dt)=cot(x)cos(t)

\frac{d x}{d t} = cot (x) cos (t)

derivative (x+1)e^x

d er i v a t i v e (x + 1) e^{x}

limit as x approaches 0 of sin(x)ln(4x)

x \to 0 lim (sin (x) ln (4 x))

integral of (In(x+1))/(sqrt(x+1))

\int \frac{I n ( x + 1 )}{x + 1} d x

(4+x)(dy)/(dx)=9y

(4 + x) \frac{d y}{d x} = 9 y