derivative y=(x-1)(x^2+x+1)

Lösung

ableitung von

y = (x - 1) (x^{2} + x + 1)

3 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 1, g = x^{2} + x + 1

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

\frac{d}{d x} (x - 1) = 1

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

= 1 \cdot (x^{2} + x + 1) + (2 x + 1) (x - 1)

Vereinfache

1 \cdot (x^{2} + x + 1) + (2 x + 1) (x - 1) : 3 x^{2}

= 3 x^{2}

\frac{d y}{d x} = \frac{2 x}{y + 1}

\int_{1}^{1000} \frac{25}{x ^{3}} d x

x^{2} y^{^{'}} + 2 x y = ln (x), y (1) = 2

t an g e n t \frac{( x ^{2} )}{x + 2}

x \to 0 lim (\frac{cos ( \frac{π}{2} - x )}{x})