How do you compute the first order derivative of

Question

 

z=(xy^2)/(x^2)y^3)+1)?

Answer 1

z = [(xy²) / x²*y³ ]+ 1

Simplify

z = [1 / xy] + 1

Apply derivative to each side

dz  = (-1/ x²)dx(1 / y) + (-1 / y²)dy (1 / x)

Take out common term -1 / xy

dz = -1 / xy{dx / x + dy / y]

 

Answer 2

z = [(xy²) / x²*y³ ]+ 1

Simplify

z = [1 / xy] + 1

Apply derivative to each side

dz  = (-1/ x²)dx(1 / y) + (-1 / y²)dy (1 / x)

Take out common term -1 / xy

dz = -1 / xy[dx / x + dy / y]

The first order derivative dz = -1 / xy[dx / x + dy / y]