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Beliebt Rechnen >

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

Lösung

\frac{d}{d x} (ln (x^{s i n (x)}))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (ln (x^{s i n (x)}))

Wende die Kettenregel an:

\frac{1}{x ^{s i n (x)}} \frac{d}{d x} (x^{s i n (x)})

= \frac{1}{x ^{s i n (x)}} \frac{d}{d x} (x^{s i n (x)})

\frac{d}{d x} (x^{s i n (x)}) = x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

= \frac{1}{x ^{s i n (x)}} x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

Vereinfache

\frac{1}{x ^{s i n (x)}} x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x}) : cos (x) ln (x) + \frac{sin ( x )}{x}

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

Graph

Beliebte Beispiele

integral of 1/(xsqrt(9x-1))

\int \frac{1}{x 9 x - 1} d x

integral of ((cos(x))/(sin(2x)))

\int (\frac{cos ( x )}{sin ( 2 x )}) d x

derivative (x+1770)/(30(x+2))

d er i v a t i v e \frac{x + 1770}{30 ( x + 2 )}

derivative of 2x(3x-2^4)

\frac{d}{d x} (2 x (3 x - 2)^{4})

integral of (t^5)/(t^6+1)

\int \frac{t ^{5}}{t ^{6} + 1} d t