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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{1}{( s ^{2} + 4 ) ( s ^{2} + 1 )}

x \to 4 - lim (c x^{2} + 9 x)

\int 1 + \frac{4 x ^{2}}{( 1 - x ^{2} ) ^{2}} d x

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = - 7

\frac{\partial}{\partial y} (3.25 yz cos (x yz))