Determine the derivative of the following function with resp

Determine the derivative of the following function with respect to x:

f(x,y,z) = 3x^2 yz + e^-2y cos(3y) + 3y^2 + 4z^2 (e^-2z)

Solution

In partial derivatives, the variables other than the one we differentiate with (y and z here)are treated as constants

Therefore, when we have to diffrentiate the finction wuth respect to x, y and z will be considered as constants

df/dx =(d/dx)(3x²yz +e^-2ycos(3y) +3y²+4z²+e^-2z) =6xyz+0+0+0+0=6xyz

Answer is 6xyz