derivative of 3arcsin(x^2)

Lösung

\frac{d}{d x} (3 arcsin (x^{2}))

\frac{6 x}{1 - x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (3 arcsin (x^{2}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (arcsin (x^{2}))

Wende die Kettenregel an:

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

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

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

= 3 \cdot \frac{1}{1 - ( x ^{2} ) ^{2}} \cdot 2 x

Vereinfache

3 \cdot \frac{1}{1 - ( x ^{2} ) ^{2}} \cdot 2 x : \frac{6 x}{1 - x ^{4}}

= \frac{6 x}{1 - x ^{4}}

\int_{1}^{2} 4^{x} d x

a re a 4 x^{2}, \frac{x}{2}

x \to 0 - lim (- x + 3)

\int_{- 1}^{1} π (1 - x^{2}) d x

x \to \infty lim (1.003)