Question Se z=e^{\frac{x}{y}} \operatorname{sen}\left(\frac{x}{y}\right)+e^{\frac{y}{x}} \cos \left(\frac{y}{x}\right), mostre que x \frac{\delta z}{\delta x}+y \frac{\delta z}{\delta y}=0
Passo 1
O enunciado dá
z = e^{\frac{x}{y}}\sin\!\bigl(\tfrac{x}{y}\bigr)\;+\;e^{\frac{y}{x}}\cos\!\bigl(\tfrac{y}{x}\bigr)