If h(x) = 2xsin(2x), find h'(x).

Differentiate using product rule as expression consist of two functions.Product Rule: d(f(x)g(x))/dx = g(x).f'(x) + f(x).g'(x)Chain Rule: d(f(g(x)))/dx = g'(x) . f'(g(x))
Let: f(x) = 2x f'(x) = 2 - simple differentiation g(x) = sin(2x) g'(x) = 2cos(2x) - chain rule as function is composite
Therefore: h'(x) = sin(2x).2 + 2x.2cos(2x)
Final Answer: h'(x) = 2sin(2x) + 2xcos(2x)