2 2 Equal derivatives ?Verify that the functions f(x) = sin x and g(x) = ?cos x have the same derivative. What can you say about the diffe? rence ? ?f ?? ? Explain.

Solution 36AE Step 1 In this problem we have to verify whether the functions f(x) = sin xand 2 g(x) = cos x have same derivative. 2 2 Given f(x) = sin xand g(x) = cos x f (x) = 2 sin x cos xand g (x) = 2 cos x (sin x) = 2sin x cos x That is f (x) = g(x) Hence f(x)and g(x)have same derivative.