Learning Materials
Features
Discover
Chapter 12: Q. 23 (page 944)
Use the definition of the partial derivative to find the partial derivatives specified in Exercises 23–26.
when localid="1650225390806" .
The partial derivative is.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Given a function of three variables, and a constraint equation how many equations would we obtain if we tried to optimize f by the method of Lagrange multipliers?
Fill in the blanks to complete the limit rules. You may assume that and exists and that k is a scalar.
Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.
Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.
Construct examples of the thing(s) described in
the following.
Try to find examples that are different than
any in the reading.
(a) A function z = f(x, y) for which ∇f(0, 0) = 0 but f is
not differentiable at (0, 0).
(b) A function z = f(x, y) for which ∇f(0, 0) = 0 for every
point in R2.
(c) A function z = f(x, y) and a unit vector u such that
Du f(0, 0) = ∇f(0, 0) · u.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App