(\partial)/(\partial y)((9x-4y)(12x+2y))

解答

\frac{\partial}{\partial y} ((9 x - 4 y) (12 x + 2 y))

- 30 x - 16 y

求解步骤

\frac{\partial}{\partial y} ((9 x - 4 y) (12 x + 2 y))

将

x

视为常数

使用微分乘法定则:

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

f = 9 x - 4 y, g = 12 x + 2 y

= \frac{\partial}{\partial y} (9 x - 4 y) (12 x + 2 y) + \frac{\partial}{\partial y} (12 x + 2 y) (9 x - 4 y)

\frac{\partial}{\partial y} (9 x - 4 y) = - 4

\frac{\partial}{\partial y} (12 x + 2 y) = 2

= (- 4) (12 x + 2 y) + 2 (9 x - 4 y)

化简

(- 4) (12 x + 2 y) + 2 (9 x - 4 y) : - 30 x - 16 y

= - 30 x - 16 y

d er i v a t i v e 8 a^{6} - 14 a^{3} - 15

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t an g e n t f (x) = 2 x^{2} - x^{4}, (1, 1)

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n = 1 \sum \infty \frac{6}{n ( n + 1 )}