derivative of 1/3 x^3+1/2 x^2-6x+8

Lösung

\frac{d}{d x} (\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 6 x + 8)

x^{2} + x - 6

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 6 x + 8)

Vereinfache

\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 6 x + 8 : \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x + 8

= \frac{d}{d x} (\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x + 8)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{3}}{3}) + \frac{d}{d x} (\frac{x ^{2}}{2}) - \frac{d}{d x} (6 x) + \frac{d}{d x} (8)

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

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

\frac{d}{d x} (6 x) = 6

\frac{d}{d x} (8) = 0

= x^{2} + x - 6 + 0

Vereinfache

= x^{2} + x - 6

y^{^{'}} = x sin (x) + x cos (x)

l a pl a ce t r an s f or m cos (4 x)

t an g e n t - \frac{6}{( 3 x + 5 ) ^{2}}

(y + x cot (\frac{y}{x})) d x - x d y = 0

x \to 6 lim (\frac{( \frac{1}{x} - \frac{1}{6} )}{x - 6})