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Vigorous derivative? (Posted on 2023-06-26) Difficulty: 3 of 5
Let f(x) = (1 + x)√(2 + x2)∛(3 + x3). Determine f'(1) and f'(-1).

No Solution Yet Submitted by Danish Ahmed Khan    
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The long way - solution Comment 1 of 1
Using the chain rule for derivatives (twice in succession) and then evaluating with Excel:

f'(-1)= 2.182247  and f'(1)=5.957161 to six significant fifures after the decimal point.
I confirmed this by calculating the local slope of the function using a very small delta around both -1 and 1.

For an exact answer:
f'(-1) = (3^.5) * (2^(1/3))
f'(1) = (3^.5)*(4^(1/3))+2*(3^.5)/(4^(2/3))+2*(4^(1/3))/(3^(.5))

Evaluating these matched the numeric answers above within the number of places shown.

  Posted by Kenny M on 2023-06-27 12:16:14
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