(\partial)/(\partial x)(3sin(2xy))

解答

\frac{\partial}{\partial x} (3 sin (2 x y))

6 y cos (2 x y)

求解步骤

\frac{\partial}{\partial x} (3 sin (2 x y))

将

y

视为常数

将常数提出:

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

= 3 \frac{\partial}{\partial x} (sin (2 x y))

使用连锁律:

cos (2 x y) \frac{\partial}{\partial x} (2 x y)

= cos (2 x y) \frac{\partial}{\partial x} (2 x y)

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

= 3 cos (2 x y) \cdot 2 y

化简

= 6 y cos (2 x y)

x \to \infty lim (e^{8 x})

\frac{d}{d x} ((2 x^{3} + 9 x)^{5})

\int 12 x^{2} - 5 x + 4 d x

\int_{- 2}^{2} \frac{1}{x ^{2} + 4} d x

\frac{d}{d x} (e^{2 x + 5} + \frac{1}{e ^{x^{2}}})