d/(dy)(x^3+3xy^2-15x-12y)

解答

\frac{d}{d y} (x^{3} + 3 x y^{2} - 15 x - 12 y)

6 x y - 12

求解步骤

\frac{d}{d y} (x^{3} + 3 x y^{2} - 15 x - 12 y)

将

x

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d y} (x^{3}) + \frac{d}{d y} (3 x y^{2}) - \frac{d}{d y} (15 x) - \frac{d}{d y} (12 y)

\frac{d}{d y} (x^{3}) = 0

\frac{d}{d y} (3 x y^{2}) = 6 x y

\frac{d}{d y} (15 x) = 0

\frac{d}{d y} (12 y) = 12

= 0 + 6 x y - 0 - 12

化简

= 6 x y - 12

d er i v a t i v e - 9.8 t^{2} + 2 t + 1

\frac{d}{d x} (\frac{55}{0.01 x ^{2} + 1})

\frac{\partial}{\partial x} (f (x, y) (\frac{x}{y}))

\frac{d}{d a} (sin^{2} (a) cos^{2} (a))

y^{^{'}} + y = \frac{1}{1 + e ^{2 x}}