SOLUTION: Differentiate the following expression implicitly: (1+e^3x)^2 = 3+ln(x+y)

Question 1155753: Differentiate the following expression implicitly: (1+e^3x)^2 = 3+ln(x+y)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Fortunately, you will never see an equation like this anywhere except in a math class, as an exercise in various concepts of calculus.

Find the derivative using implicit differentiation, using power and chain rules, among other things.

[1]

We can't leave the "y" in that expression, so we need to solve the original equation for y.

[2]

Now substitute [2] in [1].

Note as a further exercise in this kind of thing, you can use equation [2] above and differentiate it directly; that of course will give you the same answer.

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