Compute the derivative of (f º g) if
f(u) = 7·u+1, g(x) = sin(6·x)
Recall the chain rule for differentiating (f º g)(x):
(f º g)'(x) =(f(g(x)))' = (g(x))·
In order to substitute appropriately into the chain rule to compute,
(f º g)'(x) = (f(g(x)))' = f'(g(x))g'(x),
we need to find f'(g(x)), which is f'(u) evaluated at g(x) = sin(6·x).
f(u) = 7·u+1
f'(u) =
Applying the chain rule, find the derivative of (f º g) where
f(u) = 7·u+1 and g(x) = sin(6·x)
with
f'(g(x)) = 7 and g'(x) = 6·cos(6·x).
(f º g)'(x) = f'(g(x))g'(x) = ·cos(·x)