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

Multivariable chain rule intro

Problem

Suppose we have a vector-valued function g, left parenthesis, t, right parenthesis and a scalar function f, left parenthesis, x, comma, y, comma, z, right parenthesis. Let h, left parenthesis, t, right parenthesis, equals, f, left parenthesis, g, left parenthesis, t, right parenthesis, right parenthesis.
We know:
g(1)=(0,2,4)g(1)=(1,6,2)f(0,2,4)=(3,5,1)\begin{aligned} &g(1) = (0, 2, 4) \\ \\ &g'(1) = (-1, 6, 2) \\ \\ &\nabla f(0, 2, 4) = (3, 5, 1) \end{aligned}
Evaluate start fraction, d, h, divided by, d, t, end fraction at t, equals, 1.
h, prime, left parenthesis, 1, 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?