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

Lösung

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

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

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 - x ^{2}}{( 1 + x ^{2} ) ^{2}}

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

Vereinfache

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

= \frac{1 - x ^{2}}{( x ^{2} + 1 ) x ^{4} + x ^{2} + 1}

\frac{d}{d x} (\frac{( 2 π - x cos ( x ) )}{x - 2 π})

e x p an d \frac{( 3 x ^{2} - 4 ) ( x ^{2} - 6 )}{x ^{2} + 4}

\frac{\partial}{\partial y} (\frac{x}{y + x})

\frac{d}{d x} ((x^{2} + 3)^{s i n (x)})

l a pl a ce t r an s f or m e^{3 t} (9 - 4 t + 10 sin (\frac{t}{2}))