Find dy/dx for the following, presenting your answer in its simplest form: y = (3x^2) + (3x sin(x)) + 4

Split into three separate derivatives: dy/dx = d/dx(3x²) + d/dx(3x sin(x)) + d/dx(4) Apply rule: d/dx(xⁿ) = nx^(n-1) to first and third terms - second term needs more work: dy/dx = (6x) + d/dx(3x sin(x)) + 0 Apply above rule to second term whilst also applying the product rule: (f g)' = (f' g) + (f g') Note: standard derivative d/dx (sin(x)) = cos(x) dy/dx = (6x) + (3sin(x)) + (xcos(x)) Finally, simplify via factorisation: dy/dx = 3[(2x) + (sin(x)) + (xcos(x))] dy/dx = 3[sin(x) + x(2 + cos(x))] Final note, majority of parenthesis/brackets are extraneous, yet used for clarity of what each term encompasses.