derivative of (e^x/(sin(x)))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{e ^{x}}{sin ( x )} : e^{x} csc (x)

= \frac{d}{d x} (e^{x} csc (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = csc (x)

= \frac{d}{d x} (e^{x}) csc (x) + \frac{d}{d x} (csc (x)) e^{x}

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= e^{x} csc (x) + (- cot (x) csc (x)) e^{x}

Vereinfache

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

d er i v a t i v e sec^{2} (x) - tan^{2} (x)

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

n = 2 \sum \infty \frac{1}{n ^{n}}

n = 0 \sum \infty (1 + \frac{1}{n})^{n}

\frac{d}{d x} (3 sec (5 x))