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Beliebt Rechnen >

derivative of log_{sqrt(e)}(sin(x))

Lösung

\frac{d}{d x} (lo g_{e} (sin (x)))

Lösung

2 cot (x)

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (sin (x)))

Vereinfache

lo g_{e} (sin (x)) : 2 ln (sin (x))

= \frac{d}{d x} (2 ln (sin (x)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (ln (sin (x)))

Wende die Kettenregel an:

\frac{1}{sin ( x )} \frac{d}{d x} (sin (x))

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

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

= 2 \cdot \frac{1}{sin ( x )} cos (x)

Vereinfache

2 \cdot \frac{1}{sin ( x )} cos (x) : 2 cot (x)

= 2 cot (x)

Graph

Beliebte Beispiele

laplacetransform t(tcos(t)-sin(t))

l a pl a ce t r an s f or m t (t cos (t) - sin (t))

limit as x approaches 2 of (x^2-3x+2)/(x^2+5x-14)

x \to 2 lim (\frac{x ^{2} - 3 x + 2}{x ^{2} + 5 x - 14})

laplacetransform t^2*e^{-4t}

l a pl a ce t r an s f or m t^{2} \cdot e^{- 4 t}

integral of sin^4(x)cos^2(x)

\int sin^{4} (x) cos^{2} (x) d x

steigung (22,54),(62,27)

s l o p e (22, 54), (62, 27)