Find fx
 and fy
 for

f(x,y)=(1−x+y)e^x+2y

Let's find the partial derivatives \( f_x \) and \( f_y \) for the function \( f(x, y) = (1 - x + y)e^x + 2y \).

### 1. Finding \( f_x \) (the partial derivative with respect to \( x \)):

Given:
\[
f(x, y) = (1 - x + y)e^x + 2y
\]

Differentiate \( f(x, y) \) with respect to \( x \):

\[
f_x = \frac{\partial}{\partial x} \left[ (1 - x + y)e^x + 2y \right]
\]

Apply the product rule to the term \((1 - x + y)e^x\):

\[
f_x = \frac{\partial}{\partial x}(1 - x + y) \cdot e^x + (1 - x + y)

Learn how to find the partial derivatives fx and fy for the function f(x, y) = (1 - x + y)e^x + 2y with a step-by-step solution. This problem covers partial derivatives and the product rule, suitable for advanced high school and college students.

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