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.
Skin Changes From Lupus. You can have skin lupus with or without having full-blown systemic lupus erythematosus (SLE), the most common kind of lupus. Be on the lookout for some of these rashes that can be caused by skin lupus: Butterfly rash: Called a malar rash, this may spread over your nose and cheeks in the shape of a butterfly. The butterfly rash can be just a faint blush or a very severe, scaly rash. The sun's UV rays can trigger it and make it worse. Sores and rashes. Some may be coin-shaped (called discoid lupus). Or you may develop red, scaly patches or a red, ring-shaped rash, especially where your skin gets sun or other UV light. The sores get worse without treatment.