use implicit differentiantion to find the derivative of the fuction
cos(x^2+2y) + xe^y = 0
"cos(x^2+2y) + xe^y = 0"
"\\frac{d}{dx}[cos(x^2+2y) + xe^y]=\\frac{d}{dx}[0]"
"\\frac{d}{dx}[cos(x^2+2y) + xe^y]=\\frac{d}{dx}[0]"
"(-sin(x^2+2y)).\\frac{d}{dx}[x^2+2y]+\\frac{d}{dx}[e^y].x+e^y.\\frac{d}{dx}[x]=0"
"-(\\frac{d}{dx}[x^2]+\\frac{d}{dx}[2y])sin(x^2+2y)+e^y.\\frac{d}{dx}[y].x+e^y.1=0"
"-(2x+2y\\prime)sin(x^2+2y)+e^yy\\prime x+e^y=0"
"-(2y\\prime +2x)sin(2y+x^2)+xe^yy\\prime +e^y=0"
"y\\prime =\\frac{2xsin(2y+x^2)-e^y}{2sin(2y+x^2)-xe^y}"
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