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

Lösung

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

4 x^{3} + 3 x^{2} + 2 x + 1

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (1) = 0

= 4 x^{3} + 3 x^{2} + 2 x + 1 + 0

Vereinfache

= 4 x^{3} + 3 x^{2} + 2 x + 1

\int x 3^{x^{2}} d x

s l o p e f (x) = 2 - \frac{4}{x}

\int 4 sin^{2} (2 x) d x

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

\frac{d y}{d x} = e^{y} cos (2 x)