find the derivative of f(x)=sin5xcos4x

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We need to solve this using the product and chain rules.For the product rule, let p = sin(5x) and q = cos(4x)We'll need the derivatives of p and q as well, so let's find them with the chain rule:p' = 5cos(5x)q' = 4(-sin(4x)) = -4sin(4x)Thus f'(x) = pq' + qp' = [sin(5x)][-4sin(4x)] + [cos(4x)][5cos(5x)] = -4sin(5x)sin(4x) + 5cos(4x)cos(5x) orf'(x) = 5cos(4x)cos(5x) - 4sin(5x)sin(4x)