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 20230627 12:16:14 