(\partial)/(\partial x)(-3cos(pix)+6x^2y+5e^{xz}+3yz-98)

解答

\frac{\partial}{\partial x} (- 3 cos (π x) + 6 x^{2} y + 5 e^{x z} + 3 yz - 98)

12 x y + 5 e^{x z} z + 3 π sin (π x)

求解步骤

\frac{\partial}{\partial x} (- 3 cos (π x) + 6 x^{2} y + 5 e^{x z} + 3 yz - 98)

将

y, z

视为常数

使用微分加减法定则:

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

= - \frac{\partial}{\partial x} (3 cos (π x)) + \frac{\partial}{\partial x} (6 x^{2} y) + \frac{\partial}{\partial x} (5 e^{x z}) + \frac{\partial}{\partial x} (3 yz) - \frac{\partial}{\partial x} (98)

\frac{\partial}{\partial x} (3 cos (π x)) = - 3 π sin (π x)

\frac{\partial}{\partial x} (6 x^{2} y) = 12 y x

\frac{\partial}{\partial x} (5 e^{x z}) = 5 e^{x z} z

\frac{\partial}{\partial x} (3 yz) = 0

\frac{\partial}{\partial x} (98) = 0

= - (- 3 π sin (π x)) + 12 y x + 5 e^{x z} z + 0 - 0

化简

= 12 x y + 5 e^{x z} z + 3 π sin (π x)

\int x - \frac{8}{x} d x

t a y l or ln^{2} (1 + x)

\int \frac{1}{361 - x ^{2}} d x

\frac{d y}{d x} - \frac{y}{x} = x e^{x}, y (1) = e - 1

x \to \infty lim (\frac{1}{4 x})