derivative arcsin(cos(x^3))

Lösung

ableitung von

arcsin (cos (x^{3}))

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

Schritte zur Lösung

\frac{d}{d x} (arcsin (cos (x^{3})))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{1 - cos ^{2} ( x ^{3} )} (- sin (x^{3}) \cdot 3 x^{2}) : - \frac{3 x ^{2} sin ( x ^{3} )}{sin ^{2} ( x ^{3} )}

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

t an g e n t f (x) = 3 x - 2 x, at x = 1

\frac{\partial}{\partial y} (\frac{9 y}{x ^{5}})

y^{^{''}} + 22 y = 0

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

a re a 10 - 7 x, y = 0, x^{2} - 20