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Beliebt Rechnen >

derivative of arcsin(cos(x))

Lösung

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

Lösung

- csc (x) sin^{2} (x)

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

Vereinfache

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

= - csc (x) sin^{2} (x)

Graph

Beliebte Beispiele

(\partial)/(\partial x)(e^{-(x+y)})

\frac{\partial}{\partial x} (e^{- (x + y)})

xy^'=2x^2y+3x^3e^{x^2}

x y^{^{'}} = 2 x^{2} y + 3 x^{3} e^{x^{2}}

limit as x approaches infinity of xln(1)

x \to \infty lim (x ln (1))

derivative (2x-5)/(sqrt(x))

d er i v a t i v e \frac{2 x - 5}{x}

(dy)/(dx)=2xsqrt(x-7)

\frac{d y}{d x} = 2 x x - 7