The numeric value of the derivative of the function at x = -1 is given by:
f'(-1) = -12.
Derivative of product rule
A function defined by the multiplication of two functions is as follows:
f(x) = g(x)h(x)
The derivative of this function is given as follows:
f'(x) = g'(x)h(x) + h'(x)g(x).
In this problem, the function is:
f(x) = x^6h(x).
The parameters are as follows:
The derivative is given by:
f'(x) = x^6h'(x) + 6h(x)x^5
At x = -1, the numeric value of the derivative of the function is:
f'(-1) = (-1)^6 x (6) + 6 x 3 x (-1)^5 = 6 - 18 = -12.
We just took the general derivative calculated, and for the numeric value at x = -1, only the data given on the exercise for function h(x) was needed.
More can be learned about derivatives at https://brainly.com/question/5313449
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