Question

o vetor gradiente da função f, dada por f (x,y) = ylny/x²

Answer 1

$\frac{\partial }{\partial x}( \frac{ylny}{x^2} })= \frac{-2ylny}{x^3}\\ \frac{\partial }{\partial y}(\frac{ylny}{x^2} })= \frac{ln y}{x^2} +y \frac{1}{y} \frac{1}{x^2} \\ = \frac{1}{x^2}\\ \bigtriangledown f(x,y)=\frac{\partial f }{\partial x}i+\frac{\partial f }{\partial y}j\\ \bigtriangledown f(x,y)= (\frac{-2ylny}{x^3})i+ (\frac{1}{x^2}) j$

Answer 2

Resposta correta no AVA