Find dy/dx by implicit differentiation
Let's find the derivative. So d dx of e x squared y equals the derivative of x plus y. So what we have here is a product rule. So we end up having x squared y prime plus 2xy e to the x squared y is equal to one plus y prime. So we want to get the y prime's on the same side here.
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This could get a little tricky. So what's gonna happen next is we multiply these together. So we have y prime x squared e to the x squared y is equal to one plus y prime minus 2xye x squared y. And now all this is just going to be divided by, so y prime is equal to one plus y prime minus 2xye x squared y divided by x squared e to the x squared y, but we’ve made a huge mistake and now need to subtract minus y prime over here.
So what we end up getting is y prime quantity x squared e to the x squared y minus one is equal to one minus 2xye to the x squared y. So y prime is equal to one minus 2xye to the x squared y divided by x squared e to the x squared y minus one. That's it!