derivative y=sqrt(x)+x^{3/2}-8x

Lösung

ableitung von

y = x + x^{\frac{3}{2}} - 8 x

\frac{1}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2} - 8

Schritte zur Lösung

\frac{d}{d x} (x + x^{\frac{3}{2}} - 8 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x) + \frac{d}{d x} (x^{\frac{3}{2}}) - \frac{d}{d x} (8 x)

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

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

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

= \frac{1}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2} - 8

(5 x^{3} + 3 x y + 2 y^{2}) d x + (x^{2} + 2 x y) d y = 0

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

x \to 0 lim (ln (2 x^{2} + x))

\int \frac{x}{x ^{2} + 49} d x

in v erse l a pl a ce \frac{1}{( s - 3 ) ( s - 9 )}