(\partial)/(\partial x)((sin(x+y))/(y^2))

解答

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

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

求解步骤

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

将

y

视为常数

将常数提出:

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

= \frac{1}{y ^{2}} \frac{\partial}{\partial x} (sin (x + y))

使用连锁律:

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

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

\frac{\partial}{\partial x} (x + y) = 1

= \frac{1}{y ^{2}} cos (x + y) \cdot 1

化简

\frac{1}{y ^{2}} cos (x + y) \cdot 1 : \frac{cos ( x + y )}{y ^{2}}

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

4 \frac{d y}{d x} - 12 x^{2} = 0

d er i v a t i v e y = \frac{80}{x ^{6}}

d er i v a t i v e y = 3 x + 2 cos (x)

\int 6 e^{4 x} d x

\frac{\partial}{\partial x} ((x - y)^{n})