derivative of 1/(sqrt(x^2-9y^2))

Lösung

\frac{d}{d x} (\frac{1}{x ^{2} - 9 y ^{2}})

- \frac{x - 9 y \frac{d y}{d x}}{( x ^{2} - 9 y ^{2} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{2} - 9 y ^{2}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x^{2} - 9 y^{2})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x ^{2} - 9 y ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} - 9 y^{2})

= - \frac{1}{2 ( x ^{2} - 9 y ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} - 9 y^{2})

\frac{d}{d x} (x^{2} - 9 y^{2}) = 2 x - 18 y \frac{d y}{d x}

= - \frac{1}{2 ( x ^{2} - 9 y ^{2} ) ^{\frac{3}{2}}} (2 x - 18 y \frac{d y}{d x})

Vereinfache

- \frac{1}{2 ( x ^{2} - 9 y ^{2} ) ^{\frac{3}{2}}} (2 x - 18 y \frac{d y}{d x}) : - \frac{x - 9 y \frac{d y}{d x}}{( x ^{2} - 9 y ^{2} ) ^{\frac{3}{2}}}

= - \frac{x - 9 y \frac{d y}{d x}}{( x ^{2} - 9 y ^{2} ) ^{\frac{3}{2}}}

\frac{d}{d x} ((1 - x^{2})^{10})

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

s l o p e (- \frac{2}{7}, \frac{2}{3}), (\frac{5}{7}, - \frac{7}{3})

x \to 1 lim (\frac{x - 1}{x ^{n} - 1})

(x + y)^{2} d x + (2 x y + x^{2} - 4) d y = 0