derivative P(x)=x(x-8)(x+5)

解答

导数

P (x) = x (x - 8) (x + 5)

3 x^{2} - 6 x - 40

求解步骤

\frac{d}{d x} (x (x - 8) (x + 5))

使用微分乘法定则:

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

f = x, g = (x - 8) (x + 5)

= \frac{d x}{d x} (x - 8) (x + 5) + \frac{d}{d x} ((x - 8) (x + 5)) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 8) (x + 5)) = 2 x - 3

= 1 \cdot (x - 8) (x + 5) + (2 x - 3) x

化简

1 \cdot (x - 8) (x + 5) + (2 x - 3) x : 3 x^{2} - 6 x - 40

= 3 x^{2} - 6 x - 40

\int_{0}^{2} (\frac{x}{( 3 - x ) ^{2}}) d x

y^{^{'}} = 3 y + x e^{x}

\int 2 arctan (\frac{y}{x}) d x

\int \frac{x ^{3} + 3 x ^{2} + 5 x + 4}{x ^{2} + 3 x + 2} d x

in v erse l a pl a ce \frac{( 10 )}{5 \cdot s ^{2} + 7 s}