- #1
jonjacson
- 453
- 38
Homework Statement
The equation is z= e (x*y), the interesting thing is y is function of x too, y = ψ(x)
Calculate the partial derivative respect to x, and the total derivative.
Homework Equations
Total differential:
dz= ∂z/∂x dx + ∂z/∂y dy
The Attempt at a Solution
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Well, according to the book:
∂z/∂x= y * exy
But I don't agree with this result, because if y is also function of x this term will be different.
For example if y=x3, z would be = ex4, and the partial derivative is:
∂z/∂x = 4 x3 * e x4
and this is not the same as:
y * e xy = x3ex4
What do you think?
I just want to check if the book is right, this topic (multivariate differential calculus) is so important that I want to understand it correctly.