derivative of 1/((x^2+1^{3/2)})

Lösung

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

- \frac{3 x}{( x ^{2} + 1 ) ^{\frac{5}{2}}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{3}{2 ( x ^{2} + 1 ) ^{\frac{5}{2}}} \frac{d}{d x} (x^{2} + 1)

= - \frac{3}{2 ( x ^{2} + 1 ) ^{\frac{5}{2}}} \frac{d}{d x} (x^{2} + 1)

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

= - \frac{3}{2 ( x ^{2} + 1 ) ^{\frac{5}{2}}} \cdot 2 x

Vereinfache

- \frac{3}{2 ( x ^{2} + 1 ) ^{\frac{5}{2}}} \cdot 2 x : - \frac{3 x}{( x ^{2} + 1 ) ^{\frac{5}{2}}}

= - \frac{3 x}{( x ^{2} + 1 ) ^{\frac{5}{2}}}

f (x) = \frac{1 - 5 x}{x + 3}

\frac{d}{d x} (x^{\frac{8}{x}})

x \to π lim (ln (cos (x) - 8))

l a pl a ce t r an s f or m cos (5 t)

x \to 2 lim (\frac{x}{( - x + 2 ) ^{2}})