derivative of 1/3 x^3+1/2 x^2+2

Lösung

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

x^{2} + x

Schritte zur Lösung

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

Vereinfache

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

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

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} (2)

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

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

\frac{d}{d x} (2) = 0

= x^{2} + x + 0

Vereinfache

= x^{2} + x

y^{^{''}} - \frac{2}{x} y^{^{'}} - \frac{10}{x ^{2}} = 0

\int \frac{26}{( x - 1 ) ( x ^{2} + 25 )} d x

\int \frac{2 x - 3}{4 x - x ^{2}} d x

\int_{e}^{e^{2}} \frac{1}{x ln ( x )} d x

\frac{d}{d x} (\frac{40}{1 + 79 e ^{- x}})