derivative of x^3-3x^2+3x-3

Lösung

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

3 x^{2} - 6 x + 3

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\frac{d}{d x} (3) = 0

= 3 x^{2} - 6 x + 3 - 0

Vereinfache

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

x \to 0 + lim ((1 + 4 x)^{\frac{5}{x}})

im pl i c i t \frac{d y}{d x}, y^{5} = x^{7}

d er i v a t i v e x^{2} + 3 x + \frac{1}{x ^{2}}

\int \frac{arcsin ( 4 x )}{1 - 16 x ^{2}} d x

\frac{d}{d r} (r + 7 r)