Find (dy)/(dx) For this ☟ y = cos(xy) ​

Question

Find

`(dy)/(dx)`
For this ☟

`y = cos(xy)`
​

Answer 1

`(dy)/(dx)=(-y\sin xy)/(1+\sin xy)`

Explanation:

`(dy)/(dx)=-(d)/(dx) (xy) \sin(xy) \\ \\ =-\left(x (dy)/(dx)+y \right) \sin(xy) \\ \\ =-x (dy)/(dx) \sin(xy)-y\sin(xy) \\ \\ (dy)/(dx)(1+x\sin(xy))=-y \sin xy \\ \\ (dy)/(dx)=(-y\sin xy)/(1+\sin xy)`