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Beliebt Rechnen >

derivative of arcsin(sqrt(sin(x)))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sin (x)) = \frac{cos ( x )}{2 sin ( x )}

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(df)/(dx)=tan^3(x)-sec^3(x)

\frac{df}{d x} = tan^{3} (x) - sec^{3} (x)

sum from n=1 to infinity of (80)/(8^n)

n = 1 \sum \infty \frac{80}{8 ^{n}}

integral of 4e^{x+y}

\int 4 e^{x + y}

tangent y=x^2-5,(-5,20)

t an g e n t y = x^{2} - 5, (- 5, 20)

derivative f(x)= 1/(t^2)

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