Find the equation of the tangent plane to the surface Z e2x

Find the equation of the tangent plane to the surface Z = e2x/17 ln(4y) at the point(3,1,1.973). z=

Solution

dz/dx = (2/17)e^2x/17ln(4y) = (2/17)*e^6/17ln(4) = 0.232

dz/dy = e^2x/17/y = e^6/17/1 = 1.423

So the tangent plane is:

z - 1.973 = 0.232(x-3) + 1.423(y-1)

Or

z = 0.232x + 1.423y - 0.146