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

Lösung

ableitung von

1 - x^{2} arcsin (x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 - x^{2}, g = arcsin (x)

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (\frac{( x - y )}{c ( a - b )})

\frac{d}{d t} (8 t)

\int_{6}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

\frac{\partial}{\partial x} (ln (5 x + 2 y))

t an g e n t 3 x^{2} - 4 x