If f and g are differentiable function such that f(2)=3, f'(2)=-1, f'(3)=7, g(2)=-5, and g'(2)=2, find (g-f)'(2).
I don't need to know this exact answer - if some could just tell me where to find the rules for this kind of math, that'd be great, thanks.

Question

If f and g are differentiable function such that f(2)=3, f'(2)=-1, f'(3)=7, g(2)=-5, and g'(2)=2, find (g-f)'(2).
I don't need to know this exact answer - if some could just tell me where to find the rules for this kind of math, that'd be great, thanks.

freckles · Answer

$$(g-f)'(x)=g'(x)-f'(x) \text{ by difference rule }$$

freckles · Answer

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CB4QFjAAahUKEwiModjc_dTHAhWVD5IKHcf5DBs&url=http%3A%2F%2Ftutorial.math.lamar.edu%2Fpdf%2FCalculus_Cheat_Sheet_Derivatives_Reduced.pdf&ei=VyflVcyZO5WfyATH87PYAQ&usg=AFQjCNFzH7Fl-YNE7BsQ18rwU51DEp_IQA&sig2=5ZP8oAv8a5OglAOkamXD0w first page look under basic rules

anonymous · Answer

There we go. THERE we go. I was so confused when a later part used (fg)'(2) and it wasn't just (f)'(2) x (g)'(2). Thanks.

freckles · Answer

np yeah (fg)' needs product rule :)