Problem 04 | Exact Equations Jhun Vert Sun, 05/10/2020 - 08:34 pm

Problem 04
$(y^2 - 2xy + 6x) \, dx - (x^2 - 2xy + 2) \, dy = 0$
 

Problem 03 | Exact Equations Jhun Vert Sun, 05/10/2020 - 08:32 pm

Problem 03
$(2xy - 3x^2) \, dx + (x^2 + y) \, dy = 0$
 

Problem 02 | Exact Equations Jhun Vert Sun, 05/10/2020 - 08:27 pm

Problem 02
$(6x + y^2) \, dx + y(2x - 3y) \, dy = 0$
 

Problem 01 | Exact Equations Jhun Vert Sun, 05/10/2020 - 08:26 pm

Problem 01
$(x + y) \, dx + (x - y) \, dy = 0$
 

01 Maximum area of triangle of given perimeter Jhun Vert Fri, 05/08/2020 - 10:48 pm

Problem 1
Show that the largest triangle of given perimeter is equilateral.
 

Partial Derivatives

Partial Differentiation with Respect to One Variable

Let F be a function of several variables, say x, y, and z. In symbols,

$F = f(x, \, y, \, z)$.

The partial derivative of F with respect to x is denoted by

$\dfrac{\partial F}{\partial x}$

and can be found by differentiating f(x, y, z) in terms of x and treating the variables y and z as constants.