`sin(x) + 2cos(2y) = 1` Find `dy/dx` by implicit differentiation.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`sinx+2cos(2y)=1`

Differentiating both sides with respect to x,

`cosx+2(-sin(2y)d/dx(2y))=0`

`cosx+2(-2sin(2y)dy/dx)=0`

`cosx-4sin(2y)dy/dx=0`

`4sin(2y)dy/dx=cosx`

`dy/dx=cosx/(4sin(2y))`

kandukurimaths | Student

 

`2cos(2y)=1-sin(x)`

`-4sin(2y)dy/dx=-cos(x)`

` dy/dx=cos(x)/(4sin(2y))`

``