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Beliebt Rechnen >

derivative of ln(sin(e^x))

Lösung

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

Lösung

e^{x} cot (e^{x})

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{sin ( e ^{x} )} cos (e^{x}) e^{x}

Vereinfache

\frac{1}{sin ( e ^{x} )} cos (e^{x}) e^{x} : e^{x} cot (e^{x})

= e^{x} cot (e^{x})

Graph

Beliebte Beispiele

derivative g(x)=ln(3x)

d er i v a t i v e g (x) = ln (3 x)

derivative 9x^{1/3}+9/2 x^{4/3}

d er i v a t i v e 9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}}

(\partial)/(\partial x)(-xe^{(xy)})

\frac{\partial}{\partial x} (- x e^{(x y)})

integral of-2x+18x^2-4x^3+C

\int - 2 x + 18 x^{2} - 4 x^{3} + C d x

integral of 2cos^3(x)sin(x)

\int 2 cos^{3} (x) sin (x) d x