derivative f(x)=x^{-1/2}+x^{1/2}

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

in v erse l a pl a ce \frac{1}{s ^{3} + s ^{2} + s}

d er i v a t i v e y = x^{3} - x

d er i v a t i v e f (x) = cos (4 t + 12)

x \to 0 lim (\frac{y ^{1 - x}}{1 - x})

y^{^{''}} - 6 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1