dérivée de (x^3-4x^2-6x+1(x^2-3x+1))

Solution

\frac{d}{d x} ((x^{3} - 4 x^{2} - 6 x + 1) (x^{2} - 3 x + 1))

5 x^{4} - 28 x^{3} + 21 x^{2} + 30 x - 9

étapes des solutions

\frac{d}{d x} ((x^{3} - 4 x^{2} - 6 x + 1) (x^{2} - 3 x + 1))

Appliquer la règle du produit:

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

f = x^{3} - 4 x^{2} - 6 x + 1, g = x^{2} - 3 x + 1

= \frac{d}{d x} (x^{3} - 4 x^{2} - 6 x + 1) (x^{2} - 3 x + 1) + \frac{d}{d x} (x^{2} - 3 x + 1) (x^{3} - 4 x^{2} - 6 x + 1)

\frac{d}{d x} (x^{3} - 4 x^{2} - 6 x + 1) = 3 x^{2} - 8 x - 6

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

= (3 x^{2} - 8 x - 6) (x^{2} - 3 x + 1) + (2 x - 3) (x^{3} - 4 x^{2} - 6 x + 1)

Simplifier

(3 x^{2} - 8 x - 6) (x^{2} - 3 x + 1) + (2 x - 3) (x^{3} - 4 x^{2} - 6 x + 1) : 5 x^{4} - 28 x^{3} + 21 x^{2} + 30 x - 9

= 5 x^{4} - 28 x^{3} + 21 x^{2} + 30 x - 9

\frac{d}{d x} (x (2 x + 3)^{5})

13 e^{4 t} e^{2}

\frac{d}{d x} (\frac{x - 3}{x + 4})

\int_{1}^{e} ln (3 x) d x

\frac{d}{d x} (tan^{3} (x) + tan (x^{3}))