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.
There are other skin diseases that can occur in lupus and in other autoimmune diseases. Those include vasculitis and alopecia (hair loss). Mucosal ulcers in the nose or mouths are another common symptom of lupus. Like other symptoms, ulcers can come and go as the disease flares.