(\partial)/(\partial x)(arcsin(x/(y^2)))

Lösung

\frac{\partial}{\partial x} (arcsin (\frac{x}{y ^{2}}))

\frac{1}{y ^{4} - x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (arcsin (\frac{x}{y ^{2}}))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{1 - ( \frac{x}{y ^{2}} ) ^{2}} \frac{\partial}{\partial x} (\frac{x}{y ^{2}})

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

\frac{\partial}{\partial x} (\frac{x}{y ^{2}}) = \frac{1}{y ^{2}}

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

Vereinfache

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

= \frac{1}{y ^{4} - x ^{2}}

d er i v a t i v e y = e^{π}

x \to \frac{π}{2} lim ((sin (x) - cos (x))^{t a n (x)})

\int 8 x e^{9 x} d x

x \to 0 lim (\frac{( 484 + x ) ^{0.5} - 22}{x})

t an g e n t f (x) = x^{4} - 10 x^{2} + 9, at x = 2