Question

Use implicit differentiation to find dy/dx. e^4x = sin(x+2y).

This is a practice problem. It says the correct answer is 4e^x/(2sin(x+2y)) but I keep getting 4e^(4x)/(2cos(x+2y)).

I thought the derivative of e^(4x) would be 4e^(4x), not 4e^(x).

And I use chain rule on sin(x+2y) but I get cos(x+2y) * 2dy/dx.

Help would be appreciated, thanks!

Answer 1

e^(4x) = sin(x+2y)
4e^(4x) = cos(x+2y) * <b>(1 + 2 dy/dx)</b>
4e^(4x) = cos(x+2y) + 2 dy/dx cos(x+2y) , I expanded

dy/dx = (4e^(4x) - cos(x+2y) ) / (2cos(x+2y))

looks like the supplied answer is wrong in more than one part.
I also "bolded" that part that you had wrong