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The Chain rule is given by: d[f(g(x))]/dx = f'(g(x)).g'(x)
In this class, we see the chain rule applied in three ways to get the following:
a) d/dx[u(x)n] = n(u(x))n-1u'(x)
b) d/dx[eu(x)] = u'(x)eu(x)
c) d/dx [ln(u(X))] = u'(x)/u(x)
1. Give an example of each of the three formulas above.
2. Explain how each one follows from the general chain rule. What is f(x) and what is g(x) in each of the formulas?
The probability of a couple getting a boy child is 0.5 and getting a girl is 0.65 . If the couple plans to get three children find the probability that at least there is a boy.
Mary works due north of home. Her husband Ben works due east. They leave at the same time, Mary is 5 miles from home, the distance between them is 1 mile more than Ben's distance from home. How far from home is Ben?
The problem states: Find dw/dt (a) using the appropriate chain rule and (b) by converting w to a function of t before differentiating.
Draw a linear production possibilities frontier representing the tradeoff between hot dogs and hot dog buns in this hypothetical economy with 120 million workers available with only 40 million workers now producing hot dogs
critical thinking paper revisednbspwrite a four to six 4-6 page 1000-1200 word paper that presents a reasoned
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A certain plane can fly 210 mph in calm air. If the plane can travel 540 miles against the wind in the same amount of time it can travel 810 miles with the wind, then what is the rate of the wind?
Write a 1,050- to 1,400-word paper in which you research two-three companies and do the following: Evaluate the internal and external environments of each company using an environmental scan.
The demand is currently 600 t-shirts, but euphoria over the championship is subsiding so the demand is dropping by 200 t-shirts per day. How is the profit changing with respect to time?
Consider the closed interval [0,1]. Remove the open interval 11 I which has center at 1/ 2and length 1/ 2 . 2 Then remove 12 I and 22 I from 11 I ? I so that their centers coincide with the center of closed interval of 11 [0,1]? I and their length 1/..
Draw the state transition diagram for this chain. If we know P(X1 =1)= P(X1= 2)=1/ 4. find P(X1= 3) and Is this chain irreducible?
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