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February 21st, 2014, 03:45 AM  #1 
Newbie Joined: Jul 2013 Posts: 21 Thanks: 0  Some values of derivative of unknown function f?
The table shows some values of the derivative of an unknown function f. Complete the table by finding (if possible) the derivative of each transformation of f. a) g(x) = f(x) 2 b) h(x) = 2f(x) c) r(x) = f(3x) d) s(x) = f(x+2) x  2 1 0 1 2 3 f'(x) 4 2/3 1/3 1 2 4 g'(x)       h'(x)       r'(x)       s'(x)       How to do this please? Can you tell me what to do and answer the first few boxes/blanks for me, so I can learn from them and do the rest? Thank you 
February 21st, 2014, 04:53 AM  #2  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 5  Re: Some values of derivative of unknown function f? Quote:
(a) (f(x)+ g(x))'= f'(x)+ g'(x) and if g happens to be a constant, g(x)= c, its derivative is 0 so (f(x)+ c)'= f'(x). (b) (cf(x))'= cf'(x) for c a constant. (c) The chain rule: f(g(x))= f'(g(x))g'(x) and here g(x)= 3x. (d) Chain rule again but now g(x)= x+ 2.  

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derivative, function, unknown, values 
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