derivative of (e^{x^3}/(sin(2x)))

Lösung

\frac{d}{d x} (\frac{e ^{x^{3}}}{sin ( 2 x )})

3 e^{x^{3}} x^{2} csc (2 x) - 2 e^{x^{3}} cot (2 x) csc (2 x)

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x^{3}}}{sin ( 2 x )})

Vereinfache

\frac{e ^{x^{3}}}{sin ( 2 x )} : e^{x^{3}} csc (2 x)

= \frac{d}{d x} (e^{x^{3}} csc (2 x))

Wende die Produktregel an:

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

f = e^{x^{3}}, g = csc (2 x)

= \frac{d}{d x} (e^{x^{3}}) csc (2 x) + \frac{d}{d x} (csc (2 x)) e^{x^{3}}

\frac{d}{d x} (e^{x^{3}}) = e^{x^{3}} \cdot 3 x^{2}

\frac{d}{d x} (csc (2 x)) = - cot (2 x) csc (2 x) \cdot 2

= e^{x^{3}} \cdot 3 x^{2} csc (2 x) + (- cot (2 x) csc (2 x) \cdot 2) e^{x^{3}}

Vereinfache

= 3 e^{x^{3}} x^{2} csc (2 x) - 2 e^{x^{3}} cot (2 x) csc (2 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{2 x}

a re a y = x, y = 3 x, x + y = 4

\int sin (x + 2) d x

\int x 3 x - 2 d x

x \to 0 - lim (\frac{x ^{2}}{8} - \frac{4}{x})