170k views
5 votes
Let f(x, y, z) = x + ln(2y + 3z 2 ). Compute ∂f ∂x, ∂ 2f ∂y∂x, and ∂ 3f ∂z∂y∂x. Evaluate ∂ 2f ∂y∂x(2, 1, −2).

User Divanov
by
8.3k points

1 Answer

3 votes

Answer:

Explanation:

Given that


f(x, y, z) = x + ln(2y + 3z^2 )

Let us find partial derivatives one by one


(∂f )/(∂x) =1\\(∂^2f )/(∂y∂x) =(∂ )/(∂y)(1) =0\\(∂^3f )/(∂z∂y∂x) =(∂ )/(∂z)(0) =0

At the point (2,1,-2)


(∂^2f )/(∂y∂x)=0

(since at all points the value is constant 0)

User Loaf
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories