# calculus

posted by robert

find the total differential of the function
f(x,y)= xye^(x+y)

1. Steve

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]

## Similar Questions

1. ### calculus-differential equation

Consider the differential equation: (du/dt)=-u^2(t^3-t) 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=?
2. ### Differential Calculus

(1) lim x^3 - 125/x5 x^2 - 25 (2)find the inverse of the function f(x)=7x+5
3. ### calculus

Find the differential dy of the given function: y=xcosx would this just be dy=(cosx-xsinx)dx
4. ### differential calculus

use the product rule to find the derivatives of the given function y=(3x^2-8)^2
5. ### differential calculus

find the implicit function of x^3+3^y=3xy
6. ### calculus

find the total differential of the function. f(x,y) = 5y/x-y
7. ### calculus

find the solution of the initial value problem y'=xye^x; y(1)=1
8. ### calculus

Find the total differential for f(x,y,z)= cos(4x+3y+2z+1)
9. ### calculus

find the differential dy of the given function y=3x-4 sec(2x-1)
10. ### 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 population …

More Similar Questions