derivative of cos(arcsin(4x))

Lösung

\frac{d}{d x} (cos (arcsin (4 x)))

- \frac{16 x}{1 - 16 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (cos (arcsin (4 x)))

Vereinfache

cos (arcsin (4 x)) : 1 - 16 x^{2}

= \frac{d}{d x} (1 - 16 x^{2})

Wende die Kettenregel an:

\frac{1}{2 1 - 16 x ^{2}} \frac{d}{d x} (1 - 16 x^{2})

= \frac{1}{2 1 - 16 x ^{2}} \frac{d}{d x} (1 - 16 x^{2})

\frac{d}{d x} (1 - 16 x^{2}) = - 32 x

= \frac{1}{2 1 - 16 x ^{2}} (- 32 x)

Vereinfache

\frac{1}{2 1 - 16 x ^{2}} (- 32 x) : - \frac{16 x}{1 - 16 x ^{2}}

= - \frac{16 x}{1 - 16 x ^{2}}

\frac{d}{d x} (14 x^{6} - 5 x^{4} + 15 x^{2} - 8)

d er i v a t i v e f (x) = x e^{3 x^{2}} + 1

t an g e n t \frac{4}{x ^{5}} - \frac{1}{x ^{2}}

\int \frac{cos ( x )}{1 + 8 sin ( x )} d x

\frac{d y}{d x} = (\frac{x}{y})