derivative of 1/2 e^{x/2}

Lösung

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

\frac{1}{4} e^{\frac{x}{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2} e^{\frac{x}{2}} \frac{1}{2} : \frac{1}{4} e^{\frac{x}{2}}

= \frac{1}{4} e^{\frac{x}{2}}

y^{^{''}} + 4 y^{^{'}} = 5

\int \frac{4}{x} + csc (x) cot (x) d x

\frac{d}{d x} (\frac{4 x}{1 + x ^{2}})

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

x \to 1 + lim (\frac{4}{x ^{(1 - x)}})