(\partial)/(\partial y)(4cos(x^2+y^2))

解答

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

- 8 y sin (x^{2} + y^{2})

求解步骤

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

将

x

视为常数

将常数提出:

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

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

使用连锁律:

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

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

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

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

化简

= - 8 y sin (x^{2} + y^{2})

x \to 0 lim (\frac{ln ( 1 + 5 x )}{x})

y^{^{'}} - \frac{y}{x} = 0

\int (4 x + 3) \cdot (2 x^{2} + 3 x)^{3} d x

\int \frac{( x ^{3} )}{x ^{2} + 64} d x

t an g e n t y = x^{3} - 2 x + 1, (3, 22)