Find the total differential. z = x cos(y) - y cos(x)

Solution:

When we find the total differential of a equation or a function we differentiate w.r.t all the variables present in the function”

Therefore,

dz =(𝜕z/𝜕x)dx + (𝜕z/𝜕y)dy

𝜕z/𝜕x = cosy(𝜕x/𝜕x) - y𝜕cos(x)/𝜕x

𝜕z/𝜕x = cos(y) + y sin(x)

𝜕z/𝜕y = x 𝜕cos(y)/𝜕y - cos(x)𝜕y/𝜕y

𝜕z/𝜕y = -xsin(y) - cosx

dz = [cos(y) + ysin(x)]dx - [xsin(y) + cos(x)]dy

Find the total differential. z = x cos(y) - y cos(x)

Summary:

The total differential of z = x cos(y) - y cos(x) is dz = [cos(y) + ysin(x)]dx - [xsin(y) + cos(x)]dy