derivative h(x)=(x^2-3x+2)(2x^3+1)

Lösung

ableitung von

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

10 x^{4} - 24 x^{3} + 12 x^{2} + 2 x - 3

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2} - 3 x + 2, g = 2 x^{3} + 1

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

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

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

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

Vereinfache

(2 x - 3) (2 x^{3} + 1) + 6 x^{2} (x^{2} - 3 x + 2) : 10 x^{4} - 24 x^{3} + 12 x^{2} + 2 x - 3

= 10 x^{4} - 24 x^{3} + 12 x^{2} + 2 x - 3

t an g e n t x^{3}, at x = - 1

\frac{\partial}{\partial x} (6 y x^{5} - 20 y^{2} x^{4})

a re a y = x, y = 2 x

\frac{d}{d x} ((3 x)^{\frac{1}{3}})

a re a x^{2}, 2 x - x^{2}