I need help with implicit differentiation problem

[natHenderson]

So I'm trying to find the derivative of e^2 - y = xyy^3 + e^2 - 18 using implicit differentiation
I worked out the problem until I got to this: e^x - dy/dx[y] = y^3 + 3xy^2dy/dx[y]
I don't know how to solve for dy/dx from there. I'm sorry if the formatting is wrong, this is my first post

 

[Dr.Peterson]

I suspect you didn't write what you meant, as I'd expect to see e^x in the original if it is in the derivative, and xyy^3 could have been written as xy^4. This is mostly a matter of typos rather than formatting, though you may also need to be careful with parentheses, especially around exponents.

If necessary, include an image of the actual problem, so we can be sure what it looks like.

 

[natHenderson]

Yes, you were right, the original had e^x, here's the original question, thanks!

 

[Steven G]

With respect to x can you please state the derivative of each term below so we can where you may be making a mistake.

1) e^x,
2) y,
3) xy^3
4) e^2
5) 18

Now how for e^x - y = xy^3 + e^2 - 18

 

[Dr.Peterson]

So here is your question with the equation corrected:

So I'm trying to find the derivative of y at (2, 2), given e^x - y = xy^3 + e^2 - 18, using implicit differentiation
I worked out the problem until I got to this: e^x - dy/dx[y] = y^3 + 3xy^2dy/dx[y]
I don't know how to solve for dy/dx from there. I'm sorry if the formatting is wrong, this is my first post

Your derivative looks good, except that I don't know why [y] is there; it isn't needed. So you should have

e^x - dy/dx = y^3 + 3xy^2dy/dx​

Now you just have to solve for dy/dx. If it helps, replace it with u and solve for u:

e^x - u = y^3 + 3xy^2u​

The last step will be to replace x with 2 and y with 2.