What is the implicit derivative of #3=e^y-e^(2y) #?
To compute any implicit derivative, you always want to differentiate like you normally would with respect to x, but when taking the derivative of something with a "y" in it, you must multiply by y' or dy/dx. After that, isolate for dy/dx, then you're done! If you want to take the derivative with respect to it's the same idea!
In your example you have
First, take the derivative of everything with respect to x, but remember, when taking the derivative of a term with "y" in it, you must multiply by dy/dx:
Factor out dy/dx:
That's the derivative (with respect to x)! Hopefully that helps! All in all, that's the process you should follow do calculate implicit derivatives!