# Differentiating this phrase

d/dx(E^xy+y)

## The Attempt at a Solution

How do you differentiate this phrase

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

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
Gold Member
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'.

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

or how can u tell, is what i mean

Mark44
Mentor
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
Gold Member
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.

e^(-xy)+X same for bottom

Mark44
Mentor
Much better.