Q: The first rule you probably learned for finding derivatives is the power rule. This rule says that for a variable x{\displaystyle x} raised to any exponent a{\displaystyle a}, the derivative is as follows:  f(x)=xa{\displaystyle f(x)=x^{a}} f′(x)=axa−1{\displaystyle f^{\prime }(x)=ax^{a-1}} For example, review the following functions and their derivatives:  If f(x)=x2{\displaystyle f(x)=x^{2}}, then f′(x)=2x{\displaystyle f^{\prime }(x)=2x}  If f(x)=3x2{\displaystyle f(x)=3x^{2}}, then f′(x)=2∗3x=6x{\displaystyle f^{\prime }(x)=2*3x=6x}  If f(x)=x3{\displaystyle f(x)=x^{3}}, then f′(x)=3x2{\displaystyle f^{\prime }(x)=3x^{2}}  If f(x)=12x4{\displaystyle f(x)={\frac {1}{2}}x^{4}}, then f′(x)=4∗12x3=2x3{\displaystyle f^{\prime }(x)=4*{\frac {1}{2}}x^{3}=2x^{3}} To find the derivative of a square root function, you need to remember that the square root of any number or variable can also be written as an exponent. The term below the square root (radical) sign is written as the base, and it is raised to the exponent of 1/2. Consider the following examples:  x=x12{\displaystyle {\sqrt {x}}=x^{\frac {1}{2}}} 4=412{\displaystyle {\sqrt {4}}=4^{\frac {1}{2}}} 3x=(3x)12{\displaystyle {\sqrt {3x}}=(3x)^{\frac {1}{2}}} If the function is the simplest square root, f(x)=x{\displaystyle f(x)={\sqrt {x}}}, apply the power rule as follows to find the derivative:   f(x)=x     {\displaystyle f(x)={\sqrt {x}}\ \ \ \ \ }(Write the original function.)  f(x)=x(12)     {\displaystyle f(x)=x^{({\frac {1}{2}})}\ \ \ \ \ }(Rewrite the radical as an exponent.)   f′(x)=12x(12−1)   {\displaystyle f^{\prime }(x)={\frac {1}{2}}x^{({\frac {1}{2}}-1)}\ \ \ }(Find derivative with the power rule.)  f′(x)=12x(−12)   {\displaystyle f^{\prime }(x)={\frac {1}{2}}x^{(-{\frac {1}{2}})}\ \ \ }(Simplify exponent.) At this stage, you need to recognize that a negative exponent means to take the reciprocal of what the number would be with the positive exponent. The exponent of −12{\displaystyle -{\frac {1}{2}}} means that you will have the square root of the base as the denominator of a fraction. Continuing with the square root of x function from above, the derivative can be simplified as:  f′(x)=12x−12{\displaystyle f^{\prime }(x)={\frac {1}{2}}x^{-{\frac {1}{2}}}} f′(x)=12∗1x{\displaystyle f^{\prime }(x)={\frac {1}{2}}*{\frac {1}{\sqrt {x}}}} f′(x)=12x{\displaystyle f^{\prime }(x)={\frac {1}{2{\sqrt {x}}}}}
A: Review the power rule for derivatives. Rewrite the square root as an exponent. Apply the power rule. Simplify the result.

Q: The combination of burn damage, skin grafting, and/or surgery can leave you in a great deal of pain. Depending on the nature of your wound, you may be prescribed topical, oral, or injectable pain medications. Powerful pain medications can also lead to dependency — such as opioid addiction — so follow your dosing plan to the letter and report any problems to your doctor. Signs of addiction to pain medications can include changes in sleep patterns and daily habits; drowsiness or lethargy; reduced concern for basic hygiene; personality changes; weight loss and reduced appetite; and persistent flu-like symptoms. Both of these dressings help hydrate and protect burn wounds, and are frequently prescribed for a wide range of burn injuries. If your doctor prescribes one of them as part of your wound care regimen, make sure you fully understand how to apply and change them.  Hydrocolloid dressings are simple, one-piece, sticky patches that provide a water-resistant barrier and a gel coating for the wound. Each patch can last for 3-5 days. These are more common for mild or moderate burns. Hydrogel dressings contain a hydrating polymer that must be wrapped loosely with a gauze bandage to remain in place. A single dressing can last for up to 4 days. They are more commonly prescribed for blistering wounds. It takes a lot of energy for your body to heal itself, so you need to provide it with additional healthy fuel while you recover. Protein is a great fuel for healing, so increase your intake of lean meats, nuts, beans, yogurt, eggs, tofu, and soy products.  Vitamin A, vitamin C, and zinc can also help with wound healing. Increase your intake of fresh fruits and vegetables — especially citrus for vitamin C and dark leafy greens for vitamin A — and add seafood, fortified grains, and red meats for zinc. Your doctor may also recommend a multivitamin or similar nutritional supplement. Consult a registered dietician for help in crafting the best wound healing diet for you. As you heal from your burn, you may find that your mobility and coordination are impaired by tissue damage, nerve damage, scar tissue, and chronic pain. Regular sessions of physical therapy can help improve your quality of life as you recover. A burn to your palm, for instance, can cause permanent damage that requires extensive physical therapy and training to use your hand again. Also, even as your physical scars slowly begin to fade, the emotional scars of a traumatic burn injury can last for a long time. You may benefit from psychological therapy sessions with a licensed mental health professional, or perhaps by joining a support group for burn victims.
A:
Follow your recommended pain management plan. Apply hydrocolloid or hydrogel dressings as prescribed. Eat a high protein diet and increase nutrient intake. Seek therapy for your physical and emotional needs.