find the derivative: y = (x+1/x)(x-1/x+1)
derivative rules needed for this problem: multiplication rule: derivative of the first times the second plus the derivate of the second times the first d/dx(x) = 1 d/dx(x^n) = nx^(n-1) d/dx(c) = 0 ---------------- 1. take derivative of first term: (x+1/x): derivative of x = 1 derivative of 1/x: rearrange to x^-1 derivative of x^-1 = -1x^(-1-1) = -x^-2) = 1/x^2 ans: 1+1/x^2 2. multiply the derivative of the first term (above) by the second term: (1+1/x^2)(x-1/x+1) 3.take derivative of second term: (x-1/x+1) derivative of x = 1 derivative of 1/x = 1/x^2 (steps shown above) derivative of 1 = 0 ans: 1-1/x^2 4. multiply the derivate of the second term (above) by the first term: (1-1/x^2)(x+1/x) 5. combine answers from part 2 and part 4 for final answer: (1+1/x^2)(x-1/x+1)+(1-1/x^2)(x+1/x)
multiply out: 3(4x-3)-2(3x-4).
1. distribute the 3 and -2: for the 3: 3*4x+3*(-3) for the 2, don't forget the negative sign: (-2)*3x + (-2)*(-4) 2. multiply each number together: 3*4x = 12x; 3*(-3) = -9; (-2)*3x= -6x; (-2)*(-4)=8 (remember, a negative times a negative gives you a positive) 3. combine like terms: 12x-6x = 6x; -9+8= -1 4. put it all together: 6x-1 ------------------------------- 3*4x+3*(-3)+(-2)*3x + (-2)*(-4) =12x-9-6x+8 =12x-6x-9+8 =6x-1
What is the difference between change in demanded and change in quantity demanded?
A change in demand causes a shift of the demand curve. This shift can be caused by income, price of related goods, tastes, expectations, or number of buyers. Change in quantity demanded means there is movement along the demand curve. The only thing that would cause this movement is the change in price. For example, if someone starts to make more money they will demand more of some object causing that objects demand curve to shift to the right. That is looking at a small scale of just one person, where as in economics they would do that similar process for a lot of people to determine the demand curve.