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Beliebt Rechnen >

derivative of ln(sqrt(2-2x^2))

Lösung

\frac{d}{d x} (ln (2 - 2 x^{2}))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (ln (2 - 2 x^{2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of x^4+4/3 x^3-4x^2

\frac{d}{d x} (x^{4} + \frac{4}{3} x^{3} - 4 x^{2})

integral of (-3x+2)e^{-x}

\int (- 3 x + 2) e^{- x} d x

limit as x approaches 0 of (7e^x)/(x^5)

x \to 0 lim (\frac{7 e ^{x}}{x ^{5}})

integral of 4x^2-2

\int 4 x^{2} - 2 d x

limit as x approaches+1 of 0

x \to + 1 lim (0)