((q^4)/4+(2q^3)/3-(11q^2)/2+12q)^'

Lösung

(\frac{q ^{4}}{4} + \frac{2 q ^{3}}{3} - \frac{11 q ^{2}}{2} + 12 q)^{^{'}}

q^{3} + 2 q^{2} - 11 q + 12

Schritte zur Lösung

(\frac{q ^{4}}{4} + \frac{2 q ^{3}}{3} - \frac{11 q ^{2}}{2} + 12 q)^{'}

Wende die Summen-/Differenzregel an:

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

= (\frac{q ^{4}}{4})^{^{'}} + (\frac{2 q ^{3}}{3})^{^{'}} - (\frac{11 q ^{2}}{2})^{^{'}} + (12 q)^{^{'}}

(\frac{q ^{4}}{4})^{'} = q^{3}

(\frac{2 q ^{3}}{3})^{'} = 2 q^{2}

(\frac{11 q ^{2}}{2})^{'} = 11 q

(12 q)^{'} = 12

= q^{3} + 2 q^{2} - 11 q + 12

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

d er i v a t i v e f (x) = \frac{3}{4} x

d er i v a t i v e f (x) = (arctan (8 x))^{2}

e^{5 y} y^{^{'}} = x^{3}

\int (5 x + 1)^{19} d x