How Do You Differentiate the Expression E^(xy) + y?

[bmed90]

Homework Statement

d/dx(E^xy+y)

Homework Equations

The Attempt at a Solution

How do you differentiate this phrase

 

[Char. Limit]

Well, is y a function of x? If not, it's a constant, and differentiating a constant is easy.

 

[bmed90]

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)

 

[Char. Limit]

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'.

 

[bmed90]

how are you certain that y is a function of x?

 

[bmed90]

or how can u tell, is what i mean

 

[Mark44]

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.

 

[Char. Limit]

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.

 

[bmed90]

e^(-xy)+X same for bottom

 

[Mark44]

Much better.