Solution Found!
Solution: Partial derivatives with more than two variables
Chapter 12, Problem 32E(choose chapter or problem)
Partial derivatives with more than two variables Find the first partial derivatives of the following functions.
\(g(x, y, z)=2 x^{2} y-3 x z^{4}+10 y^{2} z^{2}\)
Questions & Answers
QUESTION:
Partial derivatives with more than two variables Find the first partial derivatives of the following functions.
\(g(x, y, z)=2 x^{2} y-3 x z^{4}+10 y^{2} z^{2}\)
ANSWER:Solution 32E
Step 1 of 3:
In this problem we need to find the first partial derivatives of the function g(x, y, z) = .
Given function is : g(x, y, z) =
Now we have to find the partial derivative of g(x ,y,z) with respect to x .So , in this case assume that y and z are constants.
g(x,y,z) = ()
= () - () +() , since (u+v+w) = u+v+w
= 2y () - (x) +(1) , since cf(x) = cf(x) and here y , z are constants.
= 2y(2x) - (1) +10 (0) , since C = 0 , c is constant.
= 4xy - 3
Therefore , g(x,y,z) = 4xy - 3.