True/False Quizzes for
Applied Calculus
Topic: Techniques of Differentiation
(Chapter 4)

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1. The derivative of a sum is the sum of the derivatives.
2. The derivative of a difference is the difference of the derivatives.
3. The derivative of a product is the product of the derivatives.
4. The derivative of a quotient is the quotient of the derivatives.
5. The derivative of ln (x2+1) is ln (2x).
6.
The derivative of ln (x2+1) is
1

2x
.
7. The first rule that we would use to find the derivative of f(x) = x(1+x)12 is the product rule.
8. The first rule that we would use to find the derivative of f(x) = ln (x2-1) is the product rule.
9. If the selling price of a product is raised, total revenue from sales of the product must rise due to the increased revenue per item.
10. If the selling price of a product is raised, total revenue from sales of the product must decline due to the decrease in the number of items sold.
11. The derivative of 2x is x(2x1).
12. The derivative of 2x is 2x.
13. The derivative of ex is ex.
14. In exponential growth, the rate of change is constant.
15. In exponential growth, the percentage rate of change is constant.
16. If x and y are related by an equation so that dy/dx can be expressed as a function of x only, then the graph of the equation is the graph of an function.
17. If x and y are related by an equation so that dy/dx can be expressed as function of y only, then the graph of the equation cannot be the graph of a function.
18. The graph of y = sin(x) departs from the origin at an angle of exactly 45 degrees.
19. The derivative of ln |f(x)| has the same formula as the derivative of ln f(x), but may have a larger domain.
20. If a company's profit is increasing by $3 for each additional item manufactured, and each additional worker manufactures 10 items, then the marginal product is $30 per item.

Last Updated: August, 1999
Copyright © 1999 Stefan Waner & Steven R. Costenoble