Given fxy ex2cos2y find and simplify fxxX2fyySolutionfxy e

Solution

f(x,y) = e^(x^2)*cos(2y),
differentiate partially with respect to x, we get
fx= [e^(x^2)(2x)]cos(2y),
fxx = [ 2e^(x^2) + 4e^(x^2).(x^2)]cos(2y),

differentiate partially with respect to y, we get

fy= [e^(x^2) [-sin(2y)(2)],

fyy= e^(x^2)[-cos(2y)(4)],

fyy= -4e^(x^2)cos(2y),

fxx+X^(2)*fyy = [ 2e^(x^2) + 4e^(x^2).(x^2)]cos(2y) - 4x^2.e^(x^2)cos(2y),

fxx+X^(2)*fyy = 2e^(x^2)* cos(2y)

fxx+X^(2)*fyy = 2 f(x,y)