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MathNote: 1) If y = x^n ; then dy/dx = y' = n*x^(n1) Now, `h(x) = (x^2 + 3)^3` `h'(x) = 3*2x*(x^2+3)^2` `or, h'(x) = 6x(x^2 + 3)^2` ``

MathYou need to use the product rule to evaluate the derivative of the function, such that: `f'(x) = (2x^3 + 5x)'(x  3)(x + 2) + (2x^3 + 5x)(x  3)'(x + 2) + (2x^3 + 5x)(x  3)(x + 2)'` `f'(x) = (6x^2...

MathSince the function is a product, you need to find the derivative using the product rule, such that: `f'(x) = (x^3 x)'(x^2 + 2)(x^2 + x  1) + (x^3 x)(x^2 + 2)'(x^2 + x  1) + (x^3 x)(x^2 +...

Math`g(x) = (x^2 + 3)*(x^2  4x)` `g'(x) = 2x(x^2  4x) + (2x4)(x^2 + 3)` `or, g'(x) = 2(x^3)  8(x^2) + 2(x^3) + 6x  4(x^2)  12` `or, g'(x) = 4x^3  12x^2 + 6x  12` `or, g'(x) = 2[2x^3  6x^2 + 3x...

Math`y = (3x4)*(x^3 + 5)` `y' = 3(x^2)*(3x4) + 3(x^3 + 5)` `or, y' = 9x^3  12x^2 + 3x^3 + 15` `or, y' = 12x^3  12x^2 + 15` `or, y' = 3[4x^3  4x^2 + 5]` ``

MathYou need to use the product rule to evaluate the derivative of the function, such that: `h'(t) = (sqrt t)'(1  t^2) + (sqrt t)(1  t^2)'` `h'(t)= (1  t^2)/(2 sqrt t)  2t*sqrt t` Hence, evaluating...

MathYou need to use the product rule to evaluate the derivative of the function, such that: `g'(s) = (sqrt s)'(s^2 + 8) + (sqrt s)(s^2 + 8)'` `g'(s) = (s^2 + 8)/(2 sqrt s) + 2s*sqrt s` Hence,...

Math`f(x) = (x^3)*cos(x)` `f'(x) = 3(x^2)*cos(x)  (x^3)*sin(x)` `'or, f'(x) = (x^2)*[3cos(x)  x*sin(x)]` `` ` `

Math`g(x) = sqrt(x)*sin(x)` `g'(x) = sqrt(x)*cos(x) + sinx/{2sqrt(x)}` ` <br datamcebogus="1"> ` ` `Note: If y = sqrt(x) ; then dy/dx = {1/(2sqrt(x))} If y = sinx ; then dy/dx = cosx

Math`f(x) = x/(x^2 + 1)` `f'(x) = [(x^2 +1)  2x*x]/(x^2 +1)^2` `or, f'(x) = (x^2 + 1  2x^2)/(x^2 + 1)^2` `or, f'(x) = (1x^2)/(1+x^2)^2` `` ` `

Math`g(t) = (3t^2  1)/(2t + 5)` `g'(t) = [(2t+5)*(6t)  (3t^2  1)*2]/(2t+5)^2` `g'(t) = [12t^2 + 30t  6t^2 + 2]/(2t+5)^2` `or, g'(t) = (6t^2 + 30t + 2)/(2t+5)^2` `` ` `

Jane EyreI m looking some suggestions for doing my thesis. My topic is orphans of Victorian period and the...There are several elements to doing outstandingly good work on a thesis project. These include the quality of your research, the quality of your arguments, and the quality of your writing. To take...

Child Development ProgramsAs no two children are alike, there really is no onesizefitsall answer to this. If a baby is smaller and less coordinated than might be typical for its age and fails to reach normal...

LiteratureBy definition, the protagonist is the main character. They are the one attempting to affect a change in themselves or the present situation. Then the deuteragonist comes into play. This is the...

ScienceSince metals conduct heat and electricity, therefore, electrical wires are made up of copper which is a metal. When heat is applied to metals it provides energy to additional electrons the metal...

The Chocolate WarJerry is troubled because he fears the consequences of his rebellion against Brother Leon; additionally, he is both tormented by the oppressive atmosphere of the school culture and by his inability...

Shakespeare's SonnetsThe Italian term sonetto simply means a short or little song. The fourteenline sonnet form with which later became known as the "Italian" or "Petrarchan" sonnet appears to have first been...

The Great GatsbyThe information occurs in Chapter 8, after the confrontation between Tom and Gatsby, Nick has been unable to sleep all night. He gets up when he hears a taxi going up Gatsby’s drive. He walks...

Eyes on the PrizeThe battle over the civil rights of blacks during the Civil Rights Movement was a conflict between federal and state's rights. Many states in the South wanted to govern their own way and have...

A Separate PeaceIn the book A Separate Peace, how many times does the author use the word grey? What are the page...If you are looking for the word "grey" exactly how you spelled it in the question, the book uses it exactly zero times. If the alternate spelling, "gray," is acceptable, then the author uses the...

ArtsWhen studying linguistics, the term diglossia denotes the existence of two dialects of the same language spoken in a single geographic area. Occasionally, it will refer to two languages such as...

Sinners in the Hands of an Angry GodJonathan Edwards originally wrote his sermon for his parishioners in Northampton, Massachusetts. So, initially, his address was to his own congregation. His sermon was so successful that Edwards...

Meeting at NightThe speaker of the poem "Meeting at Night" demonstrates his desire to reunite with his lover through the use of imagery, words connoting sexual desire (connotations), onomatopoeia, alliteration,...

HistoryIf we accept the premise of this question, which is that Christopher Columbus “discovered” America, then the correct answer is that he did so in 1492. There are many ways in which to argue...

HistoryThe Four Freedoms Speech was President Franklin D. Roosevelt’s State of the Union Address for 1941. Two major themes of this speech were the idea that isolationism was impossible and the idea...

HistoryThe Punic wars were a series of conflicts between Rome and Carthage during the period from 264 BC to 146 BC. The reason for the name has to do with the history of Carthage. According to ancient...

Social SciencesAtticus tells his children that it is a sin to shoot mockingbirds. His statement surprises Scout so much that she asks Miss Maudie about it. Miss Maudie agrees with Atticus, explaining that...

O. HenryHearts and Hands is a wonderful example of O. Henry's signature literary style of irony. It is like watching a magician performing slight of hand. You are presented with three characters: a U.S....

HistoryOn eNotes, we request that you ask only one question per post. As these two questions are really not closely related to one another, I will answer the second. The Second Great Awakening affected...

John Bull's Other IslandJohn Bull's Other Island by George Bernard Shaw was written in 1904. Shaw, himself Irish, wrote it for the Abbey Theater in Dublin, but Yeats and Synge didn't think it fit with their vision of a...

The GiverJonas and Gabe escape to Elsewhere, leaving the community. When Jonas finds out that Gabe is going to be released, he has to take action. He grabs the baby and goes on the run at night. He and...

SpeakMaya Angelou's novel, I Know Why The Caged Bird Sings, is often characterized as a work of autobiographical fiction. Angelou's novel is based on Paul Laurence Dunbar's poem Sympathy where he talks...

The Merchant of VeniceIf Antonio cannot pay back Shylock, Shylock demands that Antonio forfeit a pound of his flesh. The deal makes its first appearance in Act 1, Scene 3. Go with me to a notary, seal me thereYour...

LiteratureIt is a sad (also very short) poem. The poem mentions how fields of wheat have replaced the prairie flowers and grass that the buffalo need. The writer (Vachel Lindsay) starts the poem by talking...

The Cask of AmontilladoI would say that the most effective form of psychological torture in "The Cask of Amontillado" is Montresor not killing Fortunato in the cellar and then burying him. Montresor led Fortunato down...

ScienceResearch is simply a detailed and focused study, using scientific methods, to understand why something happens and/or what are its applications. Research is basically done for two purposes: to...

MacbethThe witches never tell Macbeth that he will have to murder Duncan in order to be king. But upon hearing their premonition that he will be king, this thought enters his mind. He is terrified at the...

The OresteiaThe Erinyes were the chthonic deities responsible for vengeance, responding to blood spilled on the ground with the demand that new blood should be shed in retribution. They are portrayed as three...

Brave New WorldThe main point of conditioning in Brave New World is control. By conditioning people, the government is able to control how people feel and behave. Once that is accomplished, it makes governing...

The OresteiaThe Oresteia by Aeschylus is a true trilogy containing three plays that are performed in chronological sequence. In the first play, the Agamemnon, Clytemnestra hills her husband Agamemnon, in part...

ScienceThere are a number of ways in which heat can be transmitted, including convection, conduction and radiation. Sun's rays travel through the space by radiation (since there is no medium for heat...

ScienceDuring Prophase 1 of meiosis, two chromosomes adhere to one another forming a homolog pair. This pair is arranged in a tetrad or bivalent structure because a single chromosome is made up of two...

Sociological Theories of Religion: Conflict AnalysisWithin the scholarly community, there are actually few objections to the empirical study of religion. That is not to say that scholars consider the empirical approach the only way to study...

The Road Not TakenIn the poem "The Road Not Taken" by Robert Frost, a traveler comes to a fork in the road and needs to decide which path to take. Both paths look fairly similar, but one, which is slightly more...

Things Fall ApartChinua Achebe's postcolonial novel Things Fall Apart depicts the rise of British colonialism as experienced by members of a prominent Igbo family. Okonkwo, the patriarch of this family, is...

The OdysseyAthena mentioned the great leveler while talking to Telemanchus. The goddess was trying to convince him that the gods had the ability to protect his father on his homeward journey. However, she...

Law and PoliticsA single member district is an electoral district from which only one person gets elected in a given race. All Congressional districts in the United States are single member districts. It is true...

LiteratureCarl Sandburg (1878  1967) lived and wrote during the Gilded Age, a period of significant economic growth due to industrialization, as well as of corruption, that spanned between the 1870s to the...

Miss BrillMiss Brill does come to a realization about her life and habits. At the Jardin Publique, after she overhears the young man ridiculing her and the girl mocking her fur, her dreamworld in which she...

HistoryEven though transportation was slower in antiquity and the present, and there was no instantaneous communication via the internet, people did travel widely and exchange ideas. There were two main...