Question

How do you solve this function? help please!

Answer 1

Below

Explanation:

`f = xy^2 + ln (x) y - xe^(-y^2)`

(a)

• `f_("x") = y^2 + y/x - e^(-y^2)`

• `f_("y") = 2xy + ln (x) + 2xye^(-y^2)`

(b)

• `f_("xx") = -y/x^2`

• `f_("yy") = 2x + 2xe^(-y^2) - 4xy^2e^(-y^2)`

(c)

`df = f_x dx + f_y dy`

`= (y^2 + y/x - e^(-y^2)) dx + (2xy + ln (x) + 2xye^(-y^2)) dy`