derivative of (x^2-x^2-2(x^2-x))

Lösung

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

4 x^{3} - 6 x^{2} - 2 x + 2

Schritte zur Lösung

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

Vereinfache

(x^{2} - x)^{2} - 2 (x^{2} - x) : x^{4} - 2 x^{3} - x^{2} + 2 x

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

= 4 x^{3} - 6 x^{2} - 2 x + 2

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

f (x) = x^{4} - 8 x^{3}

\frac{d}{d x} (cos (- 5 ln (- 3 x - 1)))

\int \frac{( 1 + y )}{y} d y

d er i v a t i v e f (x) = (x + 1)