Article: The chain rule is a rule for derivatives that you use when the original function combines a function within another function. The chain rule says that, for two functions f(x){\displaystyle f(x)} and g(x){\displaystyle g(x)}, the derivative of the combination of the two can be found as follows: If y=f(g(x)){\displaystyle y=f(g(x))}, then y′=f′(g)∗g′(x){\displaystyle y^{\prime }=f^{\prime }(g)*g^{\prime }(x)}. Using the chain rule requires that you first define the two functions that make up your combined function. For square root functions, the outer function f(g){\displaystyle f(g)} will be the square root function, and the inner function g(x){\displaystyle g(x)} will be whatever appears under the radical sign. For example, suppose you wish to find the derivative of 3x+2{\displaystyle {\sqrt {3x+2}}}. Define the two parts as follows:  f(g)=g=g12{\displaystyle f(g)={\sqrt {g}}=g^{\frac {1}{2}}} g(x)=(3x+2){\displaystyle g(x)=(3x+2)} To apply the chain rule to the square root of a function, you will first need to find the derivative of the general square root function:   f(g)=g=g12{\displaystyle f(g)={\sqrt {g}}=g^{\frac {1}{2}}}  f′(g)=12g−12{\displaystyle f^{\prime }(g)={\frac {1}{2}}g^{-{\frac {1}{2}}}} f′(g)=12g{\displaystyle f^{\prime }(g)={\frac {1}{2{\sqrt {g}}}}}   Then find the derivative of the second function:  g(x)=(3x+2){\displaystyle g(x)=(3x+2)} g′(x)=3{\displaystyle g^{\prime }(x)=3} Recall the chain rule, y′=f′(g)∗g′(x){\displaystyle y^{\prime }=f^{\prime }(g)*g^{\prime }(x)}, and then combine the derivatives as follows:  y′=12g∗3{\displaystyle y^{\prime }={\frac {1}{2{\sqrt {g}}}}*3} y′=12(3x+2∗3{\displaystyle y^{\prime }={\frac {1}{2{\sqrt {(3x+2}}}}*3} y′=32(3x+2{\displaystyle y^{\prime }={\frac {3}{2{\sqrt {(3x+2}}}}}
Question: What is a summary of what this article is about?
Review the chain rule for functions. Define the functions for the chain rule. Find the derivatives of the two functions. Combine the functions in the chain rule.
Article: Use a wide-tooth comb to remove snarls and tangles from your hair. You can also use a detangling spray, if necessary. There are many options for product you can use to scrunch your hair. You can use a gel, texturizing spray, sea salt spray, mousse, pomade, oil, or some other product on your hair to scrunch it. What works best for you is going to depend on your unique hair, so you should experiment with different products.  Mousse holds hair in place lightly and adds volume.  Gel is good for thick hair and has a stronger hold than mousse.  Sea salt spray is good for flat or thin hair and helps keep your hair from drying out. Put a small amount of the product into your hands and rub them together. Grab the ends of your hair and “scrunch,” as if you were crumpling a piece of paper. Do this all around your head on all the ends and work your way up (but don't apply product to your scalp).  To create extra volume, scrunch with your head upside down. Only use a small amount of product, otherwise your hair might look hard when it is dry. You can let your hair air dry or you can use a finger diffuser to dry your hair. Use the blow dryer with a diffuser attachment while you scrunch. Direct the blow dryer up the strands, toward the section of hair that is being scrunched.
Question: What is a summary of what this article is about?
Detangle your hair while it's still wet. Choose your product. Scrunch product into your hair. Let your hair air dry or diffuse it.
Article: Each time you send or order a package through FedEx, it will have a tracking number. The tracking number on your receipt will be between 12-14 digits long on your receipt or in the email. If you do not have a tracking number, look for a door tag number starting with “DT” followed by 12 numbers. As soon as log onto the FedEx website, look for the second menu option labeled Tracking and click it. Type the tracking number into the text box and click Track. A detailed list of your package’s locations will appear.  Reach the FedEx site here: https://www.fedex.com/en-us/tracking.html. If you need to look up multiple tracking numbers, click on All Tracking Services to go to the main tracking page. Click the Sign Up or Log In option on the right side of the website. Provide all of the information required to create an account so you can store and save your package searches, even if there isn’t a tracking number. A FedEx account also allows you to track packages internationally.
Question: What is a summary of what this article is about?
Look for your tracking number on the receipt or email confirmation. Type in your tracking number in the top menu of the FedEx website. Sign up for a FedEx account if you want to view all your packages easily.