Suppose that f(2) = 3 and f′(2) = 5. Find g′(2) where g(x) = 4x2f(x).

Answer 1

If g(x)=4x² f(x), then by chain rules for derivatives we get: g^'(x) = 8x f(x) + 4x² f^'(x).

Now if we plug in x=2 in the above we obtain:

g^'(2) = 16 f(2) + 16 f^'(2) = 16*3 + 16*5 = 16*8= 128.