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Math`y=ln(sqrt(x^24))` First, use the formula: `(lnu)'= 1/u*u'` Applying that formula, the derivative of the function will be: `y' =1/sqrt(x^24) * (sqrt(x^24))'` To take the derivative of the inner...

Math`y=ln(t+1)^2` `y=2ln(t+1)` `y'=2/(t+1)` The derivative of the function y is `2/(t+1).`

MathWe'll use the formula of the derivative of a product: `(uv)' = u'v+u v'.` Here `u=x^2` and `v=ln(x),` therefore `u'=2x` and `v'=1/x.` So `y'(x) = 2x ln(x) + x^2/x = 2x ln(x) + x.`

Math`y=(ln(x))^4` `y=4ln(x)` `y'=4/x` The derivative of the function y is `4/x` .

Math`h(x) = ln (2x^2+1)` First, apply the formula: `(ln u)' = 1/u * u'` So, the derivative of the function will be: `h'(x) =1/(2x^2+1)*(2x^2+1)'` To take the derivative of the inner function, apply the...

MathGiven: `g(x)=ln(x^2)` `g(x)=ln(x^2)` `g(x)=2ln(x)` `g'(x)=2/x` The derivative of g(x) is `g'(x)=2/x `

Math`f(x) = ln(x1)` To determine its derivative, use the formula: `(lnu)' = 1/u*u'` Applying this formula, the derivative of the function will be: `f'(x)=1/(x1)*(x1)'` `f'(x)=1/(x1)*1`...

Math`f(x)=ln(3x)` Take take the derivative of this function, use the formula: `(ln u)' = 1/u * u'` Applying this formula, f'(x) will be: `f'(x) = 1/(3x)*(3x)'` `f'(x)= 1/(3x) * 3` `f'(x)= 1/x`...

The Canterville GhostInitially, the family avoid talking about the ghost because of the bloodstain in the library (in Chapter Two). Washington Otis removed it with Paragon Detergent but its continual reappearance...

The OutsidersI believe the question is asking about responses or reactions a reader might typically have to the deaths in that occur in the novel. I think one typical reaction is anger. Several central and...

The Miracle WorkerIn her letter, Annie says that the greatest problem she has with Helen is how to discipline her young charge without breaking her spirit. Annie maintains that, thus far, no one else has tried to...

Of Mice and MenWhen all the men at the ranch are preparing to go after Lennie, Slim asks George: "Where you think he might of went?" George knows exactly where Lennie would have gone. Lennie would be hiding out...

PowerIn this poem, Lorde is reacting to white oppression. This comes from a real experience in which she reacted to the acquittal of a white police officer who shot and killed a tenyearold black...

ScienceHello! As I understand, a "wave" means "electromagnetic wave," or "light." These waves may reflect from a mirror (other waves also may reflect, for example waves on a water surface may reflect from...

Around the World in Eighty DaysAllahabad was between Bombay and Calcutta. Fogg was to take a Great Indian Peninsula Railway train from Bombay to Calcutta; the journey was to take three days by train. ...Leaving Bombay, it...

The Merchant of VeniceAt the end of his Act III, Scene 1 speech in which he argues a Jew feels things just as a Christian does, Shylock tells Salarino he will treat the Christians by the example set for him. In fact,...

ReferenceThe merits and drawbacks of democratic government come from the responsibility of the people themselves to choose their leaders, and thereby, sometimes directly, sometimes indirectly, choose the...

The Canterville GhostIn Chapter Two of the story, the Canterville ghost makes his first appearance. It is very early in the morning and he is patrolling the corridor while rattling his chains, the sound of which wakes...

The Crucible"Lie detector" questions should be directly designed to evoke a physical reaction that could be seen in the results. The answers to questions put forth in a polygraph test (the technical term for...

To Kill a MockingbirdIn Chapter 12, Calpurnia takes the children to First Purchase African M.E. for Sunday service. Throughout the service, Jem and Scout notice that Calpurnia is speaking differently than she does at...

HistoryNationalism and imperialism are often related. Nationalism refers to pride in one’s country. Imperialism is the desire to gain land beyond one’s borders. When countries become imperialistic,...

My Side of the MountainIn My Side of the Mountain, Sam Gribley has run away from his home in New York City in order to live off the land in the Catskill mountains. This setting is key. It could be considered another...

HistoryThis all depends on how you regard Australia's international responsibilities. Do you think that Australia has a responsibility in the Global War on Terror? Should Australia fight the Islamic...

LiteratureRobert Frost's poem "Rangefinding" is about a stray bullet from a battle that, on the way to its target, travels through nature. The poem begins, "The battle rent a cobweb diamondstrung / And cut...

LiteratureMuriel Spark's short story "You Should Have Seen the Mess" is about a young woman named Lorna who tends to dismiss anything different from her, or anyone who won't accept her, as messy. She says...

The Second Shepherds' Play"The Second Shepherds' Play" is known for its slapstick humor and serious depiction of the nativity. One example of the farcical elements in the play is when the shepherds make several unsuccessful...

The Great GatsbyIn F. Scott Fitzgerald's The Great Gatsby, how have Jay Gatsby and George Wilson been affected by...Both Jay Gatsby and George Wilson were chasing the American Dream, and both were somewhat out of touch with reality in their inability to realize that the American Dream is really a fiction....

ScienceHello! The probability density is the square of the absolute value of a wave function, in our case it is `P_d(x)=Psi(x)^2=c^2 e^(2x/L)` for positive x's and `c^2 e^(2x/L)` for negative x's. The...

HistoryHistorians recognize the ancient Egyptians as the first known society to develop drama according to our definition of drama: a performance that has "plot, characters, [and] stage directions"...

HistoryThe United States was expanding in several ways in the 1800s. One way the United States expanded was by gaining control of more land. In 1803, the United States made the Louisiana Purchase with...

The Sign of FourConan Doyle presents London as shrouded in fog and mystery in The Sign of Four. As Holmes and Watson drive to the Lyceum Theatre in Chapter 3 with Mary Morstan, they are surrounded by fog: "The...

A Good Man Is Hard to FindAs the grandmother rides with her ungrateful son, his disrespectful children, and his characterless wife on their way to a vacation in Florida, she describes an old plantation house she had once...

The Scarlet PimpernelThe Scarlet Pimpernel is the title of a historical novel by the prolific novelist and short story writer Baroness Emma Orczy (see reference link below). It is the first novel in a series of...

The Catcher in the RyeHolden Caulfield is repulsed by his brother's profession as a screenwriter. In the opening chapter, Holden explains that his brother D. B. lives in Hollywood, not far from the hospital where he is....

Law and Politics

ScienceGreat question! Actually, it's not so much that people from different "races" look different, but that people who look different were categorized into races. I think it's really important for...

LiteratureRobert Browning's concern in the poem "Meeting at Night" is to see his beloved as quietly and secretly as possible. In the first stanza, the poem describes his arduous journey to his beloved, which...

Animal FarmIn chapter seven of Animal Farm, Orwell is able to create a sense of panic and fear through his description of the pain of starvation and the terror of Napoleon. The opening to chapter seven...

ReligionWhereas Buddhism focuses on the teachings of Gautama Buddha, who they believe is enlightened, but not deity, Christianity worships Jesus Christ as the son of God. Buddhism originated from the...

Romeo and JulietWhen Tybalt sees Romeo at Lord Capulet's masquerade party, he becomes instantly enraged, feeling as though the young Montague's presence is an insult to his family's honor. He wants to confront...

StorytellingThis is such an interesting question! Let's see if we can think through five advantages and five disadvantages for these two vital forms of storytelling. First, when we tell a story, as opposed to...

Bud, Not BuddyI would say that Bud's mom is a strong woman. I do not mean physically strong with big muscles though. I mean emotionally strong. We know that she had Bud at a very young age. Bud was age 6...

BusinessThe major advantages of a market economy are that such an economy provides the greatest personal freedom for its people, gives them with the greatest possible variety and quality of goods and...

HealthThis "60 Minutes" report, aired on October 1, 2009, reports on the waste products of burning coal to create electricity. Much of this waste is coal ash, which contains mercury, arsenic, lead, and...

Still I RiseThe third stanza of Angelou's "Still I Rise" is based upon a series of similes. Throughout the poem, the narrator, an AfricanAmerican female, is making the point that nothing that white people...

The Minister's Black VeilIn the end of "The Minister's Black Veil," the townspeople fear the Reverend Mr. Hooper because of the ambiguity of secret sin and sorrow which envelops him with his refusal to remove his veil....

BusinessFirst of all, it is not at all clear that there needs to be a solution to urbanization in the least developed countries (LDCs). As we can see in the links below, many experts believe urbanization...

SciencePerhaps the best theory that explains the origins of the universe has not been imagined and stated yet. Between the Big Bang Theory and the Steady State Theory, the scientific community is fairly...

HistoryOne of the reasons that Aurangzeb's reign (16581707) led to the eventual decline of the Mughals was that he discontinued the policy of pluralism, which refers to permitting different religious...

ScienceThe big bang theory is currently the best theory of how the universe was created. The steady state model concluded that the observable universe was of a constant density because there was a source...