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Hey there,
I am having trouble understanding how to work out this question, which is x(x+y)-e^y =y^2
I have been given the working out, of which the first line is (x+y)+x(1+y^1)-e^y *y^1=2yy^1
Really not to sure what rules they used to get from a to b, so if anyone could share, that would be most appreciated :)
Nettie.L
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
with respect to y
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'.
x with respect to y. sorry, I meant y' :)
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?
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'
the original is taking the derivative w/r to x , so y is treated as a function of x
product rule with the first term, chain rule w/ the rest ...
the goal now is to algebraically solve for y', the derivative of y w/r to x ...