Product Rule. If the two functions f(x) and g(x) are differentiable (i.e. the derivative exist) then the product is differentiable and, The proof of the Product Rule is shown in the Proof of Various Derivative Formulas section of the Extras chapter.
Inflammation is the most common reason for muscle pain and aches. Any time that major inflammation exists (strep throat, hepatitis, cancer, lupus, acute heart attack, etc.), signs and symptoms often include fevers, sweats, chills, fatigue, weight loss, and various muscle aches, pains and weakness.
Lupus, like most autoimmune disorders, has periods where symptoms flare up and periods of no symptoms (or quietly active periods). If you feel major symptoms (i.e., headache, joint pain or swelling, fatigue, face rash, lesions, chest pain and shortness of breath, and fever) or a flare up coming on, check in with your doctor.