derivative y=arcsin(x)-sqrt(1-x^2)

Lösung

ableitung von

y = arcsin (x) - 1 - x^{2}

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

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}})

Vereinfache

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

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

\frac{d ^{2}}{d x ^{2}} (\frac{x}{x + 7})

t an g e n t f (x) = x + \frac{3}{x}, at x = 4

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

s l o p e in t erce pt (15, 0), (0, - 2)

\int \frac{x ^{2}}{36 - x ^{2}} d x