derivative 2sqrt(e^{(sin(w))/3)+1}

Lösung

ableitung von

2 e^{\frac{s i n ( w )}{3}} + 1

\frac{e ^{\frac{s i n ( w )}{3}} cos ( w )}{3 ( e ^{\frac{s i n ( w )}{3}} + 1 ) ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d w} (2 e^{\frac{s i n ( w )}{3}} + 1)

Entferne die Konstante:

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

= 2 \frac{d}{d w} (e^{\frac{s i n ( w )}{3}} + 1)

Wende die Kettenregel an:

\frac{1}{2 ( e ^{\frac{s i n ( w )}{3}} + 1 ) ^{\frac{1}{2}}} \frac{d}{d w} (e^{\frac{s i n ( w )}{3}} + 1)

= \frac{1}{2 ( e ^{\frac{s i n ( w )}{3}} + 1 ) ^{\frac{1}{2}}} \frac{d}{d w} (e^{\frac{s i n ( w )}{3}} + 1)

\frac{d}{d w} (e^{\frac{s i n ( w )}{3}} + 1) = \frac{1}{3} e^{\frac{s i n ( w )}{3}} cos (w)

= 2 \cdot \frac{1}{2 ( e ^{\frac{s i n ( w )}{3}} + 1 ) ^{\frac{1}{2}}} \cdot \frac{1}{3} e^{\frac{s i n ( w )}{3}} cos (w)

Vereinfache

2 \cdot \frac{1}{2 ( e ^{\frac{s i n ( w )}{3}} + 1 ) ^{\frac{1}{2}}} \cdot \frac{1}{3} e^{\frac{s i n ( w )}{3}} cos (w) : \frac{e ^{\frac{s i n ( w )}{3}} cos ( w )}{3 ( e ^{\frac{s i n ( w )}{3}} + 1 ) ^{\frac{1}{2}}}

= \frac{e ^{\frac{s i n ( w )}{3}} cos ( w )}{3 ( e ^{\frac{s i n ( w )}{3}} + 1 ) ^{\frac{1}{2}}}

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

x \to 4 - lim (x^{2} + 2)

x \to 0 - lim (\frac{2}{9 x ^{\frac{1}{3}}})

y^{^{'}} = (x + y - 4) 2

a re a y = 3 x, y = \frac{1}{x}