Mastering Tricky Derivative Problems: Solving for dy/dx with x^2*y-e^2x=sin(y)"

[blue mango]

Homework Statement

if x^2*y-e^2x=sin(y) find dy/dx

The Attempt at a Solution

I tried solving for y but that seems quite impossible so I was wondering if anyone had any other suggestions on possible solutions. Thanks

 

[Office_Shredder]

Do you know what implicit differentiation is?

 

[blue mango]

yes...thanks for reminding me of that. the left side isn't a problem but how do you differentiate sin(y) with respect to x?

 

[blue mango]

actually wouldn't it just be 0? then dy/dx is e^2x/x

 

[Office_Shredder]

You have sin(y). y is a function of x so you could write this as sin(y(x)). Then use the chain rule