derivative of arcsin(x+sqrt(1-x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Wende Regel an

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

d er i v a t i v e f (x) = e^{x} - x^{4}

n = 1 \sum \infty ln (\frac{n}{2 n + 5})

\int \frac{x ^{2} - x + 6}{x ^{3} + 3 x} d x

\frac{\partial}{\partial x} (\frac{x \cdot y}{x + y})

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 4)