(\partial)/(\partial x)(4ysin(x^2y))

解答

\frac{\partial}{\partial x} (4 y sin (x^{2} y))

8 y^{2} x cos (y x^{2})

求解步骤

\frac{\partial}{\partial x} (4 y sin (x^{2} y))

将

y

视为常数

将常数提出:

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

= 4 y \frac{\partial}{\partial x} (sin (x^{2} y))

使用连锁律:

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

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

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

= 4 y cos (x^{2} y) \cdot 2 y x

化简

4 y cos (x^{2} y) \cdot 2 y x : 8 y^{2} x cos (y x^{2})

= 8 y^{2} x cos (y x^{2})

\int_{0}^{\frac{π}{2}} sin^{3} (t) d t

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

\int_{0}^{8} 2 π x (x^{\frac{3}{2}}) d x

\int 8 x sec^{2} (x) d x

\int x sin (2 a x) d x