Calc true or false if f(x)=g(x)+c then f'(x)=g(x) if false give equation to prove?

As you typed it, obviously false. I 'll give an example:





f (x) = x^2 g (x) = x^2 + 10





now f (x) = g (x) + c





f ' (x) = 2x g (x) = x^2 + 10





as you can see, f ' (x) does not = g (x) + c








I think what you meant to type was





if f (x) = g (x) + c, then f ' (x) = g ' (x)





this is correct.Calc true or false if f(x)=g(x)+c then f'(x)=g(x) if false give equation to prove?
f(x) = g(x) + c (I'm assuming c is just a constant)


Take the derivative of both sides with respect to x:


f'(x) = g'(x) + d/dx[c]


f'(x) = g'(x) + 0


f'(x) = g'(x)





The statement is false in general, however it is true if f(x) = g(x) = e^x.





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Edit: ok, since it was a typo, the statement is true.Calc true or false if f(x)=g(x)+c then f'(x)=g(x) if false give equation to prove?
true because the derivative of any constant is 0





oh sorry i said true because i thought you had put g'(x) in the second equation. i think you meant to....but if not then the first answer is right.
let's say g(x) = x^2


so f(x) = x^2 + 5


then f'(x) = 2x which does not equal g(x).





however f'(x) = g'(x)