derivative of arctan(arcsin(sqrt(x)))

Lösung

\frac{d}{d x} (arctan (arcsin (x)))

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

Schritte zur Lösung

\frac{d}{d x} (arctan (arcsin (x)))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int 3 y^{5} y^{3} + 1 d y

x \to - 1 lim (x + 2 x^{4})

\frac{d}{d x} (a x e^{- x})

\frac{\partial}{\partial x} (ln (a x + b y))

n = 1 \sum \infty (1)^{n}