(\partial)/(\partial x)(sin(z^3)cos(xy))

解答

\frac{\partial}{\partial x} (sin (z^{3}) cos (x y))

- y sin (x y) sin (z^{3})

求解步骤

\frac{\partial}{\partial x} (sin (z^{3}) cos (x y))

将

z, y

视为常数

将常数提出:

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

= sin (z^{3}) \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

= sin (z^{3}) (- sin (x y) y)

化简

= - y sin (x y) sin (z^{3})

\int \frac{x}{( x ^{2} + 4 x + 5 ) ^{2}} d x

x^{^{''}} + 3 x^{^{'}} + 4 x = 0

\frac{d}{d x} (x^{2} + y^{4})

t an g e n t f (x) = \frac{2 x - 1}{x + 7}, at x = 2

t an g e n t f (x) = \frac{1}{2 x}, at x = 100