Find the indicated partial derivative

Question

f(xyz)= x^yz   f_z = (e,1,0) 

 

I ended getting an answer of 1 . I am not sure if this is right. 

Answer 1

Assuming you seek ∂f/∂z,

 

f(x,y,z) = x^yz

 

Take ln of both sides and then differentiate and simplify.

 

ln(f) = yz ln(x)

 

(1/f) ∂f/∂z = y ln(x)

 

∂f/∂z = fy ln(x)

 

∂f/∂z = x^yzy ln(x)

 

[What do you men by f_z = (e,1,0) ?]