derivative of arcsin(x^2-3)

Lösung

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

\frac{2 x}{- x ^{4} + 6 x ^{2} - 8}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{1 - ( x ^{2} - 3 ) ^{2}} \cdot 2 x : \frac{2 x}{- x ^{4} + 6 x ^{2} - 8}

= \frac{2 x}{- x ^{4} + 6 x ^{2} - 8}

\int \frac{2}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

in v erse l a pl a ce \frac{1}{( s \cdot ( s + 1 ) )}

\int \frac{x ^{2}}{16 + 9 x ^{2}} d x

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

\int \frac{1}{x ^{2} - 2 x + 37} d x