d/(d{x)}(({f}(x,y))(3{x}{y}-4)^2)

解答

\frac{d}{d x} ((f (x, y)) (3 x y - 4)^{2})

f (x, y) \cdot 2 (3 x y - 4) \cdot 3 y

求解步骤

\frac{d}{d x} ((f (x, y)) (3 x y - 4)^{2})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= f (x, y) \frac{d}{d x} ((3 x y - 4)^{2})

使用连锁律:

2 (3 x y - 4) \frac{d}{d x} (3 x y - 4)

= 2 (3 x y - 4) \frac{d}{d x} (3 x y - 4)

\frac{d}{d x} (3 x y - 4) = 3 y

= f (x, y) \cdot 2 (3 x y - 4) \cdot 3 y

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