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Beliebt Rechnen >

derivative of arcsin(x/4)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

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

Vereinfache

\frac{1}{1 - ( \frac{x}{4} ) ^{2}} \cdot \frac{1}{4} : \frac{1}{16 - x ^{2}}

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

Graph

Beliebte Beispiele

derivative of tan^4(3x)

\frac{d}{d x} (tan^{4} (3 x))

integral of y^3e^{-y}

\int y^{3} e^{- y} d y

(dy)/(dx)=e^{2x-1}y^2

\frac{d y}{d x} = e^{2 x - 1} y^{2}

integral of (sqrt(x^2+25))/(x^2)

\int \frac{x ^{2} + 25}{x ^{2}} d x

fläche x=y^2,x=2-y

a re a x = y^{2}, x = 2 - y