Solve f(x, y)=\frac{2 y}{y+\cos x}

简化

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

通过将变量 y 视为常数并相对于 x 微分来求一阶偏导数

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

使用微分规则 \frac{\partial}{\partial x} (\frac{f ( x )}{g ( x )}) = \frac{\frac{\partial}{\partial x} ( f ( x )) \times g ( x ) - f ( x ) \times \frac{\partial}{\partial x} ( g ( x ) )}{( g ( x ) ) ^{2}}

f_{x} = \frac{\frac{\partial}{\partial x} ( 2 y ) ( y + cos ( x ) ) - 2 y \times \frac{\partial}{\partial x} ( y + cos ( x ) )}{( y + cos ( x ) ) ^{2}}

使用 \frac{\partial}{\partial x} (c) = 0 求导数

f_{x} = \frac{0 \times ( y + cos ( x ) ) - 2 y \times \frac{\partial}{\partial x} ( y + cos ( x ) )}{( y + cos ( x ) ) ^{2}}

求值

More Steps

f_{x} = \frac{0 \times ( y + cos ( x ) ) - 2 y ( - sin ( x ) )}{( y + cos ( x ) ) ^{2}}

任何表达式乘以 0 等于 0

f_{x} = \frac{0 - 2 y ( - sin ( x ) )}{( y + cos ( x ) ) ^{2}}

求值

f_{x} = \frac{0 - ( - 2 y sin ( x ) )}{( y + cos ( x ) ) ^{2}}

Solution

More Steps

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

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