Question

If f(x, y)=log(xy+2y²-2x),find fx(2,3) and fy(2,3)

Answer 1

Hello,

$f(x, y)=log(xy+2y^2-2x)\\\\ \dfrac{\partial{ f(x,y) } }{\partial{x}}=\dfrac{y-2}{xy+2y^2-2x}* log(e)\\ \dfrac{\partial{ f(2,3) } }{\partial{x}}=\dfrac{3-2}{2*3+2*3^2-2*2}* log(e)\\ =\dfrac{0.434294481...}{20}\approx{0,02171}\\\\ \dfrac{\partial{ f(x,y) } }{\partial{y}}=\dfrac{x+4y}{xy+2y^2-2x}* log(e)\\ \dfrac{\partial{ f(2,3) } }{\partial{y}}=\dfrac{2+12}{2*3+2*3^2-2*2}* log(e)\\ =\dfrac{7*0.434294481...}{20}\approx{0,152003...}$