Question

Помогите пожалуйста. Высшая математика.

Дана формула z=ln(e^x + e^y). Показать dz/dx + dz/dy = 1

Answer 1

$z=ln(e^x+e^y)\\frac{dz}{dx}=frac{e^x}{e^x+e^y}\\frac{dz}{dy}=frac{e^y}{e^x+e^y}\\frac{dz}{dx}+frac{dz}{dy}=frac{e^x}{e^x+e^y}+frac{e^y}{e^x+e^y}=frac{e^x+e^y}{e^x+e^y}=1$



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