(c) Compute of using the Chain Rule. of дf дх дf ду дf dz. + дя дх дя ду дя дz дя (Use symbolic notation and fractions where needed.) af дл " = +
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(c) Compute ∂?∂?
using the Chain Rule.
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- Find the first and second derivative of (x^3-3x^2+5)/(x^3+1). I found the first derivative, I believe it is correct. I got: (3x(x^3-4x-2))/(x^3+1)^2 I'm just having a harder time with the second derivative. For that I got (3(3x^8-10x^6+24x^4+12x^3+3x^2-4))/((x^3+1)^2)^2Suppose a student is a carrier of the flu virus and returns to his isolated campus of 1000 students. If it is assumed that the ratio with which the virus spreads is proportional to the product of the number x of infected students by the number of uninfected students, determine the number of infected students after 6 days if it is also observed that after four days there are 50 sick students. Suppose also that no one leaves campus while the illness lasts2. (5) Use the chain rule to find the derivative of
- In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stock’s current price is £100 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let S be the price of the stock in a month. If S is between £90 and £110, the derivative is worth nothing to you. If S is less than £90, the derivative results in a loss of £100*(90-S) to you. (The factor of 100 is because many derivatives involve 100 shares.) If S is greater than £110, the derivative results in a gain of £100*(S-110) to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with a mean £2 and a standard deviation £10. Let P(big loss) be the probability that you lose at least £1,000 (that is, the price falls below £90), and let P(big gain) be the probability that you gain at least…2. (13) The derivative ofOvertaking City A has a current population of 500,000 people and grows at a rate of 3%/yr. City B has a current population of 300,000 and grows at a rate of 5%/yr.a. When will the cities have the same population?b. Suppose City C has a current population of y0 < 500,000 and a growth rate of p > 3%/yr. What is the relationship between y0 and p such that Cities A and C have the same population in 10 years?
- What are the second and third derivatives for problem 15? Thanks!Compute 1st,2nd and 3rd derivative ofThe molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10 .Assuming X and Y to be independent, find σM.
- The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10. Find μM.1) Calculate the problem in the image as an anti-derivative. Make sure to include all steps:Compute the derivative of f(x)= (ex2 +e-x2 )/(ex2 -e-x2 )