derivative of (1-x^2^{1/2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

a re a x = y^{2} - 2, x = 6 - y^{2}

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

\frac{d}{d x} (arctan (e^{x} x^{2}))

x \to 0 lim (\frac{4}{x})

t y^{^{'}} - 4 y = t^{6} e^{t}