derivative of 1/3 x^3-x^2-3x+4

Lösung

\frac{d}{d x} (\frac{1}{3} x^{3} - x^{2} - 3 x + 4)

x^{2} - 2 x - 3

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} x^{3} - x^{2} - 3 x + 4)

Vereinfache

\frac{1}{3} x^{3} - x^{2} - 3 x + 4 : \frac{x ^{3}}{3} - x^{2} - 3 x + 4

= \frac{d}{d x} (\frac{x ^{3}}{3} - x^{2} - 3 x + 4)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{3}}{3}) - \frac{d}{d x} (x^{2}) - \frac{d}{d x} (3 x) + \frac{d}{d x} (4)

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

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

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

\frac{d}{d x} (4) = 0

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

Vereinfache

= x^{2} - 2 x - 3

a re a 7 x^{4} - 7 x^{2}, 8 x^{2}, 0

\frac{\partial}{\partial y} (e^{- (x^{2} + y^{2})})

x \to 4 lim (\frac{( ln ( x ) - ln ( 4 ) )}{x - 4})

y^{^{'}} = x^{2} y^{2}

\int \frac{sin ^{2} ( x )}{cos ( x )} d x