(\partial)/(\partial x)(4ycos(xy))

解答

\frac{\partial}{\partial x} (4 y cos (x y))

- 4 y^{2} sin (y x)

求解步骤

\frac{\partial}{\partial x} (4 y cos (x y))

将

y

视为常数

将常数提出:

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

= 4 y \frac{\partial}{\partial x} (cos (x y))

使用连锁律:

- sin (x y) \frac{\partial}{\partial x} (x y)

= - sin (x y) \frac{\partial}{\partial x} (x y)

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

= 4 y (- sin (x y) y)

化简

4 y (- sin (x y) y) : - 4 y^{2} sin (y x)

= - 4 y^{2} sin (y x)

d er i v a t i v e x tan (x)

\int_{\frac{π}{2}}^{π} sin^{2} (x) d x

t an g e n t 5 - 4 x^{3}

l a pl a ce t r an s f or m {y}

\int \frac{3 x ^{2} 16 + y ^{2}}{y}