
df = ∂f/∂x dx + ∂f/∂y dy
f = xye^(x+y)
df = (ye^(x+y) + xye^(x+y)) dx + (xe^(x+y) + xye^(x+y)) dy
= e^(x+y) [ (x+1)y dx + (y+1)x dy]
or, separating the product a bit,
f = xe^x * ye^y
df = e^x(x+1)*ye^y dx + e^y(y+1)*xe^x dy
= e^x*e^y [(x+1)y dx + (y+1)x dy]posted by Steve
Respond to this Question
Similar Questions

calculus
find the total differential of the function. f(x,y) = 5y/xy 
calculus
find the solution of the initial value problem y'=xye^x; y(1)=1 
calculus
hi! just needed help on an FRQ for ap calculus ab. let me know if you have any questions for me. I'm just really confused as far as what I am meant to do. If you could walk me through it that would be amazing. THANKS!! A 
calculusdifferential equation
Consider the differential equation: (du/dt)=u^2(t^3t) a) Find the general solution to the above differential equation. (Write the answer in a form such that its numerator is 1 and its integration constant is C). u=? b) Find the 
calculus
find the differential dy of the given function y=3x4 sec(2x1) 
Differential Calculus
Given that p=(2q^25)^2. when q=3, it is increased by 0.7%. find the appropriate percentage in p. solution dp = 2(2q^25) (2dq) dp = (4x(185)(0.7%) dp = 4(13)(0.7%) am lost from here is dp=52x0.7/100= 0.364% Responses 
differential calculus
find the implicit function of x^3+3^y=3xy 
calculus
Find the total differential for f(x,y,z)= cos(4x+3y+2z+1) 
differential calculus
use the product rule to find the derivatives of the given function y=(3x^28)^2 
Differential Calculus
(1) lim x^3  125/x5 x^2  25 (2)find the inverse of the function f(x)=7x+5