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

Differential Calculus

Course: Differential Calculus > Unit 3

Lesson 1: Chain rule
Math
Differential Calculus
Derivatives: chain rule and other advanced topics
Chain rule
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

Chain rule with tables

AP.CALC: FUN‑3 (EU), FUN‑3.C (LO), FUN‑3.C.1 (EK)
Google Classroom

Problem

The following table lists the values of functions f and h, and of their derivatives, f, prime and h, prime, for the x-values minus, 1 and 2.
xf, left parenthesis, x, right parenthesish, left parenthesis, x, right parenthesisf, prime, left parenthesis, x, right parenthesish, prime, left parenthesis, x, right parenthesis
minus, 19minus, 1minus, 5minus, 6
23minus, 116
Let function G be defined as G, left parenthesis, x, right parenthesis, equals, f, left parenthesis, h, left parenthesis, x, right parenthesis, right parenthesis.
G, prime, left parenthesis, 2, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
Stuck?
Stuck?