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Beliebt Rechnen >

derivative of xarccos(1/x)

Lösung

\frac{d}{d x} (x arccos (\frac{1}{x}))

Lösung

arccos (\frac{1}{x}) + \frac{1}{x ^{2} - 1}

Schritte zur Lösung

\frac{d}{d x} (x arccos (\frac{1}{x}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arccos (\frac{1}{x})

= \frac{d x}{d x} arccos (\frac{1}{x}) + \frac{d}{d x} (arccos (\frac{1}{x})) x

\frac{d x}{d x} = 1

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

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

Vereinfache

1 \cdot arccos (\frac{1}{x}) + \frac{1}{x x ^{2} - 1} x : arccos (\frac{1}{x}) + \frac{1}{x ^{2} - 1}

= arccos (\frac{1}{x}) + \frac{1}{x ^{2} - 1}

Graph

Beliebte Beispiele

integral of ae^{-bx}

\int a e^{- b x} d x

(dy)/(dx)=y(1-0.0008y)

\frac{d y}{d x} = y (1 - 0.0008 y)

derivative of 9sqrt(x)+7

\frac{d}{d x} (9 x + 7)

6y^{''}-6y^'+39y=0

6 y^{^{''}} - 6 y^{^{'}} + 39 y = 0

limit as x approaches 0 of (1+x/2)^{3/x}

x \to 0 lim ((1 + \frac{x}{2})^{\frac{3}{x}})