Write an article based on this "Plug in (x, y) values to find (dy/dx) for any point. Use the chain rule for functions-within-functions. For equations with x, y, and z variables, find (dz/dx) and (dz/dy)."
article: Congratulations! You've differentiated your equation implicitly — not an easy task for first-timers! Using this equation to find the slope (dy/dx) for any (x, y) point is as simple as plugging in the x and y values for your point into the right side of the equation, then solving for (dy/dx). For example, let's say that we want to find the slope at the point (3, -4) for our example equation above. To do this, we would substitute 3 for x and -4 for y, solving as follows:  (dy/dx) = (-2y2 - 2x + 5)/(2(2xy + y + 4) (dy/dx) = (-2(-4)2 - 2(3) + 5)/(2(2(3)(-4) + (-4) + 4) (dy/dx) = (-2(16) - 6 + 5)/(2(2(3)(-4)) (dy/dx) = (-32) - 6 + 5)/(2(2(-12)) (dy/dx) = (-33)/(2(2(-12)) (dy/dx) = (-33)/(-48) = 3/48, or 0.6875. The chain rule is an important piece of knowledge to have when dealing with calculus problems (including implicit differentiation problems). The chain rule states that for a function F(x) which can be written as (f o g)(x), the derivative of F(x) is equal to f'(g(x))g'(x). For difficult implicit differentiation problems, this means that it's possible to differentiate different individual "pieces" of the equation, then piece together the result. As a simple example, let's say that we need to find the derivative of sin(3x2 + x) as part of a larger implicit differentiation problem for the equation sin(3x2 + x) + y3 = 0. If we think of sin(3x2 + x) as "f(x)" and 3x2 + x as "g(x)", we can find the differentiation as follows:  f'(g(x))g'(x) (sin(3x2 + x))' × (3x2 + x)' cos(3x2 + x) × (6x + 1) (6x + 1)cos(3x2 + x) Though it's not common in basic calculus, some advanced applications may require the implicit differentiation of more than two variables. For each extra variable, you'll need to find an extra derivative with respect to x. For instance, if you're working with x, y, and z, you'll need to find both (dz/dy) and (dz/dx). We can do this by differentiating the equation with respect x twice — the first time, we'll insert a (dz/dx) every time we differentiate a term with z, and the second time, we'll insert a (dz/dy) every time we differentiate a z. After this, it's just a matter of solving for (dz/dx) and (dz/dy).  For example, let's say that we're trying to differentiate x3z2 - 5xy5z = x2 + y3. First, let's differentiate with respect to x and insert (dz/dx). Don't forget to apply the product rule where appropriate!  x3z2 - 5xy5z = x2 + y3  3x2z2 + 2x3z(dz/dx) - 5y5z - 5xy5(dz/dx) = 2x 3x2z2 + (2x3z - 5xy5)(dz/dx) - 5y5z  = 2x (2x3z - 5xy5)(dz/dx) = 2x - 3x2z2 + 5y5z (dz/dx) = (2x - 3x2z2 + 5y5z)/(2x3z - 5xy5)   Now, let's do the same for (dz/dy)  x3z2 - 5xy5z = x2 + y3  2x3z(dz/dy) - 25xy4z - 5xy5(dz/dy) = 3y2  (2x3z - 5xy5)(dz/dy) = 3y2 + 25xy4z (dz/dy) = (3y2 + 25xy4z)/(2x3z - 5xy5)

Write an article based on this "Talk to Isran. Tell Isran that you want to join. Travel to Dimhollow Crypt. Make your way through the crypt. Free Serana. Fight your way out of the crypt. Travel to Icewater Jetty. Take the boat to Castle Volkihar. Decline Lord Harkon's offer. Head back to Fort Dawnguard. Talk to Isran to join the Dawnguard."
article: You'll find Isran in the center of the main room as soon as you enter the fort. He'll appreciate your enthusiasm, but he'll need you to complete some tasks before the order is ready to be joined. You're tasked with finding what the vampires were after in the cave, and to kill any that may still be there. Tolan tells you that he'll meet you there to help. Dimhollow Crypt is in the mountains of the Dawnstar to the north. You'll find it near Frostmere Crypt if you had previously visited that location. You'll encounter multiple vampires, hounds, and skeletons, as well as a frostbite spider. At the end of the crypt, you'll free Serana, who will ask you to take her to her ancestral home. This will start the next quest in the series. After freeing Serana, you'll have to fight some gargoyles, draugr, skeletons, and undead as you make your way out of the crypt. Make sure to use the Word Wall and grab any loot that you want on your way out. This is the closest location to Castle Volkihar, where Serana wants you to take her. Icewater Jetty is in the far northwest corner, near Northwatch Keep. You can take a boat from Icewater Jetty that will transport you to Castle Volkihar, which is on an island in the northern ocean. Lord Harkon will offer to turn you into a Vampire Lord, which will activate the Vampire Lord portion of the DLC quests and lock your out of joining the Dawnguard. Decline his offer and you'll be shown out of Castle Volkihar, and told never to return. You can still become a Vampire Lord later on in the Dawnguard questline. Once you've declined Lord Harkon's offer, make your way back to Fort Dawnguard. You'll find it under attack by vampires, which you'll need to help repel. After fighting off the attacking vampires, you can speak with Isran and you'll be officially entered into the Dawnguard. Your next few quests will get teh Dawnguard Fort restocked and filled with recruits.

Write an article based on this "Ensure your bees’ safety from critters with barriers. Feed your bees as necessary. Monitor the hive at regular intervals. Watch for potential problems. Harvest Honey"
article:
Winnie the Pooh and his bear friends aren’t the only animals who like honey. Protecting your bees from predators can ensure the vitality of your colony and a fruitful harvest. Use the following solutions to keep bee predators at bay:  Put up electric barriers or chicken-wire fences to keep bears, opossums, and skunks away. Elevate hives to keep opossums and skunks out of the hives. Place birdfeeders away from hives. There may be a slight gap in time between when you introduce your bees to their hive and plants begin producing nectar. During these few weeks, feed your bees with a 1:1 mixture of water and sugar. Punch holes in the top of the hive and hang small food jars with the mixture from them. This can ensure your bees have nutrition until they can access nectar. Check the hive as often as you like. This could be once between spring introduction and fall harvesting or every day if you prefer. This can ensure your hive is flourishing, building a strong comb, and doesn’t have any pests or other problems. During your check-ups of the hive, look for signs of illness, parasite infestation or other animals accessing your hive. This can help you nip potential problems in the bud before they affect your hive. Some signs of issues with your hive include:  Misplaced bars Weakened colony Visible hive beetles or wax moths on the comb Lack of larvae Deformed wings . Take out the long, flat hive frames in the fall. Scoop off the honeycomb and wax into a container or bucket with a hot knife. Then allow the honey to gradually sink to the bottom of the container and remove the wax cappings that remain. This will give you delicious, raw honey to eat and wax cappings you can turn into candles or other items.  Set the wax capping on a sieve or filter to strain out bits of the capping from the raw honey. Get an extractor if you prefer to strain your honey into a spigot and keep the wax separate.