If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Course: Multivariable calculus > Unit 2

Lesson 5: Multivariable chain rule
Math
Multivariable calculus
Derivatives of multivariable functions
Multivariable chain rule
© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

Multivariable chain rule intro

Google Classroom

Problem

Suppose we have a vector-valued function g(t) and a scalar function f(x,y,z). Let h(t)=f(g(t)).
We know:
g(1)=(0,2,4)g′(1)=(−1,6,2)∇f(0,2,4)=(3,5,1)
Evaluate dhdt at t=1.
h′(1)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi