Question

Lembrando que (lnu) = u/u , se f (x,y) = ln (x² + y²), determine (∂f )/∂x + (∂f )/∂y

Answer 1

A derivada de ln u = u'/u
A derivada ∂ ln(x²+y²)/∂x = 2x/x²+y²
A derivada ∂ ln(x²+y²)/∂y = 2y/x²+y²

A soma das derivadas será 2x/x²+y² + 2y/x²+y²
∂ ln(x²+y²)/∂x +  ∂ ln(x²+y²)/∂y = 2x+2y/x²+y²