Solve \frac{\partial}{\partial x}\left[\frac{2 y}{y+\

Tính

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

Sử dụng quy t \overset{ˊ}{\overset{a}{˘}} c ph \overset{a}{ˆ} n biệt \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}}

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

Sử dụng \frac{\partial}{\partial x} (c) = 0 đ ể t \overset{ı}{ˋ} m đ ạo h \overset{a}{ˋ} m

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

Tính

More Steps

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

Mọi biểu thức nhân với 0 đều bằng 0

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

Tính

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

Tính

More Steps

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

Solution

More Steps

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

\frac{\partial}{\partial x}\left[\frac{2 y}{y+\cos x}\right]