The second derivative of the function f ( x ) = 12 x 2 − 4 x + 7 + ln ( x ) is calculated in two steps. First, we find the first derivative, which is f ′ ( x ) = 24 x − 4 + x 1 , and then we differentiate that to obtain the second derivative. The final result is f ′′ ( x ) = 24 − x 2 1 .
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First derivative is
f' = 24x - 4
Second derivative is
** f' ' = 24 ** ;