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The Chain Rule

The Chain Rule

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Example: If tex2html_wrap_inline121 then we can find tex2html_wrap_inline123 and g(x)=x2+1 so that F(x)=f(g(x)). Therefore, tex2html_wrap_inline129

Example: If F(x)=(3x+2)5, then tex2html_wrap_inline133

The General Power Rule

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example23


example26

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Exercises:

  1. tex2html_wrap_inline149
  2. tex2html_wrap_inline151
  3. tex2html_wrap_inline153
  4. tex2html_wrap_inline155
  5. Suppose that profit function of a company is given by P(x)=-0.01x2+50x-10,000.

    1. Find the value of x that maximzies the profit. (Hint: set tex2html_wrap_inline163 and solve for x,x=2500)
    2. Determine the maximum profit. (P(2500)=52500)
    3. Use the marginal profit to estimate the profit of the 2501 unit. tex2html_wrap_inline171 i.e. there is no profit for the 2501 unit).

Wei-Chi Yang
Mon Nov 4 11:51:59 EST 1996