Exam 1

  1. Question

    What is the derivative of f(x)= x7 e3.9x , evaluated at x=0.51?

    Solution

    Using the product rule for f(x)=g(x)·h(x), where g(x):= x7 and h(x):= e3.9x , we obtain
    f'(x) = [g(x)·h(x)]'=g'(x)·h(x)+g(x)·h'(x) = 7 x7-1 · e3.9x + x7 · e3.9x ·3.9 = e3.9x ·(7 x6 +3.9 x7 ) = e3.9x · x6 ·(7+3.9x).

    Evaluated at x=0.51, the answer is
    e3.9·0.51 ·0. 516 ·(7+3.9·0.51)=1.155964.

    Thus, rounded to two digits we have f'(0.51)=1.16.