f\left(\frac{y}{x}\right) \cdot 1 + (x+y) \pdv{}{x} \left[f\left(\frac{y}{x}\right)\right]

We are asked to simplify the given expression:

\[
f\left(\frac{y}{x}\right) \cdot 1 + (x + y) \pdv{}{x} \left[ f\left(\frac{y}{x}\right) \right]
\]

### Step 1: Rewrite the expression

f\left(\frac{y}{x}\right) \cdot 1 + (x + y) \pdv{}{x} \left[ f\left(\frac{y}{x}\right) \right]

Learn how to simplify expressions involving partial derivatives and the chain rule. This problem explores multivariable calculus concepts such as the product rule and chain rule, suitable for university-level students.

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