derivative of 1/(sqrt(a^2+x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{1}{2 ( a ^{2} + x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (a^{2} + x^{2})

= - \frac{1}{2 ( a ^{2} + x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (a^{2} + x^{2})

\frac{d}{d x} (a^{2} + x^{2}) = 2 x

= - \frac{1}{2 ( a ^{2} + x ^{2} ) ^{\frac{3}{2}}} \cdot 2 x

Vereinfache

- \frac{1}{2 ( a ^{2} + x ^{2} ) ^{\frac{3}{2}}} \cdot 2 x : - \frac{x}{( a ^{2} + x ^{2} ) ^{\frac{3}{2}}}

= - \frac{x}{( a ^{2} + x ^{2} ) ^{\frac{3}{2}}}

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

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

x \to 7 lim (\frac{x - 7}{3 x ^{2} - 21 x})

\frac{\partial}{\partial x} (ln (x) + z ln (y))

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 e^{4 t}