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Differentiating this phrase

  • Thread starter bmed90
  • Start date
  • #1
99
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Homework Statement




d/dx(E^xy+y)

Homework Equations





The Attempt at a Solution



How do you differentiate this phrase
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
14
Well, is y a function of x? If not, it's a constant, and differentiating a constant is easy.
 
  • #3
99
0
its a differential equation problem. show that

e^xy+y=x-1

is a solution to the de dy/dx=(e^-xy-y)/(e^-xy+X)
 
  • #4
Char. Limit
Gold Member
1,204
14
OK, so here y is a function of x, so you need to differentiate e^(xy) using the product rule. And the derivative of y is just y'.
 
  • #5
99
0
how are you certain that y is a function of x?
 
  • #6
99
0
or how can u tell, is what i mean
 
  • #7
33,505
5,191
its a differential equation problem. show that

e^xy+y=x-1

is a solution to the de dy/dx=(e^-xy-y)/(e^-xy+X)
Please don't make us guess what the problem is. Use parentheses to indicate what the exponent on e is.

In the numerator, is it e-xy + x, or is it e-xy + x? Same question for the denominator.
 
  • #8
Char. Limit
Gold Member
1,204
14
Because dy/dx does not equal zero for all x. Therefore, y is not constant with respect to x, and therefore it is a function of x.
 
  • #9
99
0
e^(-xy)+X same for bottom
 
  • #10
33,505
5,191
Much better.
 

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