# Implicit Differentiation Question

#### RoyalFlush100

1. Homework Statement
I am told to find dy/dx by implicit differentiation where:
e^(x^2 * y) = x + y

2. Homework Equations
The above equation and the ln of it.

3. The Attempt at a Solution
e^(x^2 * y) = x + y
(x^2 * y)ln(e) = ln(x+y)
x^2 * y = ln(x+y)
x^2(dy/dx) + y(2x) = 1/(x+y) * (1 + dy/dx)
(dy/dx)[x^2 - 1/(x+y)] = 1/(x+y) - 2xy
dy/dx = (1/(x+y) - 2xy)/(x^2 - 1/(x+y))

or here: https://postimg.org/image/3k5ygbkxt/

This was marked wrong (online software). It doesn't care about simplest form and it was entered properly. So, what did I do wrong?

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#### fresh_42

Mentor
2018 Award
I got the same result without using the logarithm, only with a single quotient, i.e. expanded by $x+y$. Maybe the missing brackets in your linear notation led to the online error. Or it is expected to write $e^{x^2y}$ instead of $x+y$ in the solution.

#### RoyalFlush100

I got the same result without using the logarithm, only with a single quotient, i.e. expanded by $x+y$. Maybe the missing brackets in your linear notation led to the online error. Or it is expected to write $e^{x^2y}$ instead of $x+y$ in the solution.
I just put it in replacing x+y with e^(x^2 * y) and it worked. Thanks!

"Implicit Differentiation Question"

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