derivative of tan(arcsin(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

sec^{2} (arcsin (x)) \frac{1}{1 - x ^{2}} : \frac{1}{( 1 - x ^{2} ) ^{\frac{3}{2}}}

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

\int \frac{( 5 x - 12 )}{x ^{3} - 6 x ^{2} + 8 x} d x

x \to 1 - lim (\frac{3}{x ^{3} - 1})

x y^{^{'}} + y = 6 x y^{2}, y (1) = - 8

(x y^{2} + 3 y^{2}) d y - 2 x d x = 0

s l o p e (4, 1), (7, 10)