derivative of arcsin(x/(sqrt(1+x^2)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{z ^{4} + 10 z ^{2} + 25}{z ^{3} + 5 z} d z

\int_{0}^{\frac{π}{4}} (tan^{2} (x)) d x

x \to 8 lim (7 x + ∣ x - 8 ∣)

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

2 y^{^{''}} + 20 y^{^{'}} + 50 y = 0