You are required to post 3 substantive messages each week in the Discussion Boar

Question

You are required to post 3 substantive messages each week in the Discussion Board. The three messages must occur on at least two Individual discussion question responses and your response to your classmates during the online week count towards the class Choose one of the following statements to discuss the validity of the statement. If the statement is always true, explain why. If not, give a counterexample. a) The derivative of a sum is the sum of the derivative. b) The derivative of a constant s 0. c) The derivative of a constant times a function is 0. d) The derivative of a product is the product of the derivative. OR Explain in your own words how to differentiate using the product rule and quotient rule. Then post a function for your classmate to differentiate using one Remember to copy and paste the DQ, and then using a different font or different color to post your answers right below each part of t

Explanation / Answer

From the given question,

a) derivative of sum is sum of its derivative(TRUE)

d/dx(p+q) = d/dx(p) + d/dx(q)

b)derivative of a constant is zero.

As the value of constant doesnt changes, its rate of change is zero.

d/dx(c)=0

c)derivative of a constant times function is zero: FALSE

d/dx [ c. f(x) ]= c d/dx [ f(x) ]

d)derivative of the product is product of its derivative: TRUE

d/dx(x2*x3)=x2*d/dx(x3)+(x3) d/dx(x2)

=x2(3x2) + x3*2x

=5x4

d/dx(x5)=5x4

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