derivative 12arcsin(e^{x/2})

Lösung

ableitung von

12 arcsin (e^{\frac{x}{2}})

\frac{6 e ^{\frac{x}{2}}}{1 - e ^{x}}

Schritte zur Lösung

\frac{d}{d x} (12 arcsin (e^{\frac{x}{2}}))

Entferne die Konstante:

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

= 12 \frac{d}{d x} (arcsin (e^{\frac{x}{2}}))

Wende die Kettenregel an:

\frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} \frac{d}{d x} (e^{\frac{x}{2}})

= \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} \frac{d}{d x} (e^{\frac{x}{2}})

\frac{d}{d x} (e^{\frac{x}{2}}) = e^{\frac{x}{2}} \frac{1}{2}

= 12 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2}

Vereinfache

12 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2} : \frac{6 e ^{\frac{x}{2}}}{1 - e ^{x}}

= \frac{6 e ^{\frac{x}{2}}}{1 - e ^{x}}

d er i v a t i v e \frac{7 x}{8}

\frac{d y}{d x} + 5 y = 0, y (0) = 2

t an g e n t f (x) = x^{3} - 4 x + 6, at x = 2

\int \frac{x ^{2} + 1}{( x - 3 ) ( x - 2 ) ^{2}} d x

d er i v a t i v e f (x) = (- x^{2} + 9)^{2}