derivative 2x^3+3x^2-12x+1

Lösung

ableitung von

2 x^{3} + 3 x^{2} - 12 x + 1

6 x^{2} + 6 x - 12

Schritte zur Lösung

\frac{d}{d x} (2 x^{3} + 3 x^{2} - 12 x + 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (12 x) + \frac{d}{d x} (1)

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

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

\frac{d}{d x} (12 x) = 12

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

= 6 x^{2} + 6 x - 12 + 0

Vereinfache

= 6 x^{2} + 6 x - 12

x \to 0 + lim (x - \frac{1}{x} + 3)

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

y^{^{''}} - 6 y^{^{'}} + 25 y = 3 t - 2 cos (5 t)

\int (6 e^{7 x}) d x

\int \frac{sin ( a ) x}{c + cos ( a ) x} d x