derivative (5x+6)(6x-7)

解答

导数

(5 x + 6) (6 x - 7)

60 x + 1

求解步骤

\frac{d}{d x} ((5 x + 6) (6 x - 7))

使用微分乘法定则:

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

f = 5 x + 6, g = 6 x - 7

= \frac{d}{d x} (5 x + 6) (6 x - 7) + \frac{d}{d x} (6 x - 7) (5 x + 6)

\frac{d}{d x} (5 x + 6) = 5

\frac{d}{d x} (6 x - 7) = 6

= 5 (6 x - 7) + 6 (5 x + 6)

化简

5 (6 x - 7) + 6 (5 x + 6) : 60 x + 1

= 60 x + 1

\frac{d y}{d x} - (1 + x) (1 + y^{2}) = 0

\int 12 + 4 x - x^{2} d x

a re a f (x) = 2 x^{2} + 3, (- 1, 2)

x \to 2 lim (3 x^{2} - 1)

x \to 5 + lim (\frac{x + 1}{x - 5})