Question

Find dy/dx by implicit differentiation: e^(x/y) = 3x-y

Answer 1

\(d(e^{x/y})/dx=3-d(y)/dx \Longrightarrow d(x/y)/dx ~e^{x/y}=3-y'\\
\frac{y-xy'}{y^2}e^{x/y}=3-y'\Longrightarrow (1-\frac{xe^{x/y}}{y^2})y'=\frac{e^{x/y}}{y^2}+3\)

Answer 2

and continue the rest