Re: Finding the derivative

Are you differentiating with respect to y or with respect to x?

Overall, in order to solve the problem you have to have knowledge of what is known as Implicit Differentiation

Re: Finding the derivative

Re: Finding the derivative

Do you mean you want to differentiate x with respect to y or y with respect to x? The first is what you said but what you give would be correct if by "y^1" you mean the derivative of y with respect to x, normally written as y'. Solve for y'.

Re: Finding the derivative

x with respect to y. sorry, I meant y' :)

Re: Finding the derivative

the derivative of y w/r to x is y' or dy/dx

the derivative of x w/r to y is x' or dx/dy

one more time ... which?

Re: Finding the derivative

well, in the worked answer they have d/dy (so I'm guessing that means dx/dy). What I really want to know is how they get from that first question, to the (x+y)+x(1+y')-e^y *y'=2yy'

Re: Finding the derivative

the original is taking the derivative w/r to x , so **y is treated as a function of x**

$\displaystyle \frac{d}{dx} \left[x(x+y)-e^y =y^2\right]$

product rule with the first term, chain rule w/ the rest ...

$\displaystyle (1)(x+y) + x(1 + y') - e^y \cdot y' = 2y \cdot y'$

the goal now is to algebraically solve for y', the derivative of y w/r to x ...