Posted by Ivan on Thursday, October 28, 2010 at 6:21am.
first, recall chain rule, since there there is a function of x multiplied by another function of x (that is, x^7 and h(x)),, given a function f(x)=g(x)*h(x)
f'(x) = g'(x)*h(x) + g(x)*h'(x)
therefore, to get derivative of f(x)=x^7 *h(x), first get the derivative of x^7 multiplied by h(x) plus the derivative of h(x) [which is h'(x)] multiplied by x^7,,
since it is evaluated at -1, substitute values for h(-1) and h'(-1), which is given in the problem,,
so there,, please ask questions if there's something you did not understand,, :)
find f' (x) first of all using the product rule assuming we are differentiating with respect to x
f' (x) = x^7 (h' (x)) + 7x^6 (h(x))
so f'-1) = (-1)^7 (h'(-1)) + 7(-1)^6 (h(-1))
= -1(5) + 7(-1)^6 (8)
=-5 + 56
= 51
I don't see how they got 27
I see my error, I substituted the wrong way, should have been ...
so f'-1) = (-1)^7 (h'(-1)) + 7(-1)^6 (h(-1))
= -1(8) + 7(-1)^6 (5)
= -8 + 35
= 27
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