f'(x)=(4x)' * ln(3sin^2x^2+2) + 4x * (ln(3sin^2x^2+2))'
f'(x)=4ln(3sin^2x^2+2) + 4x * 1/(3sin^2x^2+2) * (3sin^2x^2+2)'
f'(x)=4ln(3sin^2x^2+2) + (4x)/(3sin^2x^2+2) * (3sin^2x^2)'+0
f'(x)=4ln(3sin^2x^2+2) + (4x)/(3sin^2x^2+2) * 6(sinx^2)'
f'(x)=4ln(3sin^2x^2+2) + (4x)/(3sin^2x^2+2) * 6cosx^2 * (x^2)'
f'(x)=4ln(3sin^2x^2+2) + (4x)/(3sin^2x^2+2) * 6cosx^2 * 2x
f'(x)=4ln(3sin^2x^2+2) + (48x^2cosx^2)/(3sin^2x^2+2)