Question

YsinX+e^x=Y^2 Implicit differentiation？

Answer 1

ahh now we have a question
in this case you are thinking of \(y\) as a function of \(x\) although you don't know what it is
(that is why it is "implicit" i.e. it is implied that \(y\) is a function of \(x\)
start with the product rule
\[y'\sin(x)-y\cos(x)+e^x=2yy'\] and solve for \(y'\)

Answer 2

i got this part and y'=(-ycosX-e^x)/9SinX-2y but i just wanna know the whole thing cause i got a really nasty answer at the end