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First one: f'(x) = 2x*lnx + x^2*(1/x) = 2x*lnx + x = x*(2*lnx + 1) Second derivate: f"(x) = D [x*(2*lnx + 1)] = 1*(2*lnx + 1) + x*(2/x) = 2*lnx+1+2 = 2*lnx + 3 So, there is a… minimum in this graph on point (1/e^(1/2)), -1/(2e)) = MIN(x, y) Van Sanden David Belgium (MORE)

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It is Allen and not LN as famously confused. The AllenÂ® name is a registered trademark, originated by the Allen Manufacturing Company of Hartford, Connecticut circa 1910, a…nd currently owned by Apex Tool Group, LLC. A hex key, hex wrench, Allen key, Allen wrench (also known by various other synonyms such as Inbus and Unbrako) is a tool of hexagonal cross-section used to drive bolts and screws that have a hexagonal socket in the head (internal-wrenching hexagon drive). (MORE)

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In this case, you need to apply the chain rule. Note that the derivative of ln N = 1/N. In that case we get: f(x) = ln(1 - x) âˆ´ f'(x) = 1/(1 - x) Ã— -1 âˆ´ f'(x) = -1/…(1 - x) (MORE)

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The derivative of the natural log is 1/x, therefore the derivative is 1/cos(x). However, since the value of cos(x) is submitted within the natural log we must use the chain ru…le. Then, we multiply 1/cos(x) by the derivative of cos(x). We get the answer: -sin(x)/cos(x) which can be simplified into -tan(x). (MORE)

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Most people do not mean the same thing when they write "ln" and "log". Both refer to a logarithm, but the base for "ln" is the number e (a special number roughly equal to 2.17…81) while the base for "log" is 10, unless otherwise specified. "ln" is called the natural logarithm and "log" is called the common logarithm when it refers to the base 10 logarithm. A quick example of how they are different: log 10,000 = 4 ln 10,000 = 9.21 The reason for this is that the logarithm is the inverse of (that is, it undoes) exponentiation. The first example asks "what power do I have to raise 10 to in order to get 10,000?" The exponentiation related to the first example is 104 = 10,000. The second example asks "what power do I have to raise e to in order to get 10,000?" The exponentiation related to it is e9.21 = 10,000. (MORE)

As it turns out, these stars actually regret the roles responsible for launching their careers into unforgettable stardom. After you read our explanations, perhaps you'll unde…rstand why. (MORE)

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When it comes to basic facts, what you don't know can hurt you, or at the very least surprise you.… (MORE)

As the saying goes, you can't teach an old dog new tricks. Some tricks, however, are so simple that even an old dog or new puppy can learn them. Just practice any of the follo…wing a few times a day with your dog. (MORE)

While traveling with a dog down the open road makes for good memories, doing it properly takes some thought. Help you and your dog enjoy the time you spend journeying together… by keeping these tips in mind. (MORE)

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Natural Log; It's a logarithm with a base of e, a natural constant.

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In Calculus

The definition of the natural log ln of a number is the power that you have to raise e to in order to get that number. Therefore, ln(2x+3) is the power you have to raise e… to to get 2x + 3. (MORE)

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In Calculus

If the function is (ln x)2, then the chain rules gives us the derivative 2ln(x)/x, with the x in the denominator. If the function is ln (x2), then the chain rule gives us the …derivative 2/x. (MORE)

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the 5s because it has better service but it dosent have diffrent colrs just silver gold and black

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In Calculus

ln stands for the function that associates a value with it natural logarithm or, in other words, its logarithm to the base e. You are probably familiar with common… or base 10 logarithms and know that, for instance, log10100 = 2 because 100 = 102. ln works in the same way. loge e2 = 2. The value of e is about 2.71828. Therefore, loge 2.71828 ~=1. This function has characteristics that parallel those of base 10 logarithms. You might wish to see the wikipedia page about the natural logarith. (MORE)