derivative f(x)=(x-5)(2x+5)

解答

导数

f (x) = (x - 5) (2 x + 5)

4 x - 5

求解步骤

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

使用微分乘法定则:

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

f = x - 5, g = 2 x + 5

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

\frac{d}{d x} (x - 5) = 1

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

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

化简

1 \cdot (2 x + 5) + 2 (x - 5) : 4 x - 5

= 4 x - 5

\int 8 (x + 1) \cdot ln (x + 1) d x

f (x) = \frac{10 x - 4}{3 x + 8}

t a y l or e^{- 2 x}, - 1

x \to 4 lim (\frac{x ^{2} - x}{x + 1})

x \to + 0 lim (\frac{1}{∣ x ∣})