derivative x-sqrt(2+((x+1)^2)/2)

Lösung

ableitung von

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

1 - \frac{x + 1}{2 x ^{2} + 2 x + 5}

Schritte zur Lösung

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

Vereinfache

x - 2 + \frac{( x + 1 ) ^{2}}{2} : x - \frac{x ^{2} + 2 x + 5}{2}

= \frac{d}{d x} (x - \frac{x ^{2} + 2 x + 5}{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} - \frac{d}{d x} (\frac{x ^{2} + 2 x + 5}{2})

\frac{d x}{d x} = 1

\frac{d}{d x} (\frac{x ^{2} + 2 x + 5}{2}) = \frac{x + 1}{2 x ^{2} + 2 x + 5}

= 1 - \frac{x + 1}{2 x ^{2} + 2 x + 5}

\int_{0}^{1} π (y - y^{2}) d y

d er i v a t i v e 3 t^{2} + 4 t^{5}

\frac{\partial}{\partial x} (x e^{z})

\int e^{i t} d t

x \to \infty lim (\frac{7}{x} - 1)