derivative f(x)= 1/2 x^3-2x+3

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (3) = 0

= \frac{3 x ^{2}}{2} - 2 + 0

Vereinfache

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

\int \frac{12 x ^{3} - 24 x ^{2} + 7}{x ^{2} - 2 x} d x

d er i v a t i v e \frac{s - 3}{s + 7}

x \to - 2 lim (\frac{- 1}{- x ^{2} + 4})

\frac{d y}{d x} = 4 x + \frac{9 x ^{2}}{( 3 x ^{3} + 1 ) ^{\frac{3}{2}}}

\int_{0}^{1} (3 x + 1) cos (x) d x