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Chain rule

The following table lists the values of functions ff and hh, and of their derivatives, ff' and hh', for the xx-values 00 and 22.
xxf(x)f(x)h(x)h(x)f(x)f'(x)h(x)h'(x)
0033225-53-3
2211003311
Evaluate ddx[f(h(x))]\dfrac{d}{dx}\left[f\Bigl(h(x)\Bigr)\right] at x=0x=0.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}