Find the equation of the normal to the graph at M(2,1)

[Dell]

if:
2x³+8lny+x³e^y-16-8e=0

what i did was
dy/dx=\dot{y}

6x²+8(1/y)\dot{y}+3x²e^y+x³e^y\dot{y}=0

\dot{y}=-(x²(6+3e^y)/(8/y+x³e^y)

then to find the incline of the normal, m=-1/\dot{y}

so at(2,1)

\dot{y}=-3(2+e)/2(1+e)

m(N)=2(1+e)/3(2+e)

does this seem right??

Y-1=[2(1+e)/3(2+e)]{x-2}

 

[razored]

Yes, it's correct.