derivative x^2(3x^2-x-14)

Lösung

ableitung von

x^{2} (3 x^{2} - x - 14)

12 x^{3} - 3 x^{2} - 28 x

Schritte zur Lösung

\frac{d}{d x} (x^{2} (3 x^{2} - x - 14))

Wende die Produktregel an:

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

f = x^{2}, g = 3 x^{2} - x - 14

= \frac{d}{d x} (x^{2}) (3 x^{2} - x - 14) + \frac{d}{d x} (3 x^{2} - x - 14) x^{2}

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

\frac{d}{d x} (3 x^{2} - x - 14) = 6 x - 1

= 2 x (3 x^{2} - x - 14) + (6 x - 1) x^{2}

Vereinfache

2 x (3 x^{2} - x - 14) + (6 x - 1) x^{2} : 12 x^{3} - 3 x^{2} - 28 x

= 12 x^{3} - 3 x^{2} - 28 x

\int \frac{x}{6 x ^{2} + 4} d x

in v erse l a pl a ce \frac{( s - 5 )}{s ( s + 4 ) ^{2}}

a re a y = x^{2} - 4 x + 3, x - y - 1 = 0

\int (2 x^{3} + 6 e^{x}) d x

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