May 9th, 2017, 01:05 PM  #1 
Member Joined: Feb 2017 From: henderson Posts: 36 Thanks: 0  Let h(x) = s(s(x)) Estimate
Let h(x) = s(s(x)) Estimate H'(1) dont I just simply plug in 1 or am I missing something 
May 9th, 2017, 01:11 PM  #2 
Member Joined: Feb 2015 From: Southwest Posts: 96 Thanks: 24 
I'd give it a try in just function form. They defined h(x) as a function of s(s(x)) and asked you to find h'(1). So do it, using chain rule. Remember s(x) is s'(x)x'. Once you have it, just put 1 in for the x. Remember the ' on the function means the derivative of the original function. 
May 10th, 2017, 03:56 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 
You appear to be saying you do not even understand the notation. "h(x)" is NOT the same as "H(x)" and "h'(x)" is the derivative. First, let u= s(x) so that s(s(x))= s(u). Then the derivative of h(u)= s(u), with respect to u, is, by the chain rule, s'(u)u'. Now, since s(x)= u, u'= s'(x) so the derivative of h(x)= s(s(x)), with respect to x is s'(s(x))(s'(x)). More than that cannot be done without knowing more about s(x) itself,


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