derivative of arcsin(6x^4)

Lösung

\frac{d}{d x} (arcsin (6 x^{4}))

\frac{24 x ^{3}}{1 - 36 x ^{8}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (6 x^{4}))

Wende die Kettenregel an:

\frac{1}{1 - ( 6 x ^{4} ) ^{2}} \frac{d}{d x} (6 x^{4})

= \frac{1}{1 - ( 6 x ^{4} ) ^{2}} \frac{d}{d x} (6 x^{4})

\frac{d}{d x} (6 x^{4}) = 24 x^{3}

= \frac{1}{1 - ( 6 x ^{4} ) ^{2}} \cdot 24 x^{3}

Vereinfache

\frac{1}{1 - ( 6 x ^{4} ) ^{2}} \cdot 24 x^{3} : \frac{24 x ^{3}}{1 - 36 x ^{8}}

= \frac{24 x ^{3}}{1 - 36 x ^{8}}

\frac{d}{d x} (\frac{x ^{2}}{3} + \frac{5 x}{7} - \frac{8}{5})

t an g e n t f (x) = 5 x^{3}, at x = - 2

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

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

t a y l or 4 x