Alright, so I'm having some problems. I am supposed to find dy/dx in terms of x and y by implicit differentiation. I wasn't doing too bad until I hit two problems:
Problem 1) y^2 + ye^x + e^2x=3
Problem 2) e^y^2 - x^2 - y^2=0
For the first one, I am not certain how to handle the ones to the power of x and 2x when the first one is y to the power of two. I might be overthinking it though.
For the second one, I am not certain how to handle the e^y^2, so I am just confused with that one.
Any help I can get would be much appreciated!
Alright. I couldn't get to the solution, but for the first one, what I thought is turn it into
2y + 2e(x') + 2xe^x = 3
and for the second one, if you derive it to
(y^2)(e) - 2x - 2y = 0
I'm not certain if that was the correct step to make with them or not.
1) y^2 + ye^x + e^(2x) = 3
2y(dy/dx) + e^x(dy/dx) + ye^x + 2e^(2x) = 0
2y(dy/dx) + e^x(dy/dx) = -ye^x - 2e^(2x)
(dy/dx) = [-ye^x - 2e^(2x)] / [ 2y + e^x ]
2) e^(y^2) - x^2 - y^2 = 0
2ye^(y^2)(dy/dx) - 2x - 2y(dy/dx) = 0
(dy/dx)(2ye^(y^2) - 2y) = 2x
(dy/dx) = x / [ ye^(y^2) - y]
Edited: Sorry, I didn't see your last post, I agree, give it a try by yourself first.