<Student’s name>
<University>
Question A
Find the derivatives of the following:
1)
y=cos(x2)e-2x
y'=-2xsinx2e-2x-2cosx2e-2x=-2e-2x(xsinx2+cosx2)
2)
y=2x2sin3x+4
y'=4xsin3x+4+3cos3x+42x2=2x(2sin3x+4+3xcos3x+4)
3)
y=3xsinx22x+1
y'=3sinx2+6x2cosx22x+1-6xsinx22x+12=3sinx2+6x2cosx22x+1-
-6xsinx22x+12
4)
y=x3+4x2+5x-1
y'=3x2+8x+5
Question B
- What approaches did you take to complete this assignment?
- What is the most difficult part of this assignment for you to do?
The most difficult part was #4, when I had to find the derivative of the ratio, and there was also a multiplication in numerator. This question requires being very attentive while solving it.
- How did you overcome the problem you discussed in question 2?
Just kept my mind bright and clear, and checked the solution several times to be sure.
- Have you changed your mind about mathematics in any way since you started this course? Discuss your answer.
No, I haven’t changed my mind. I am still sure that mathematics is one of the most important sciences in the world. This is much more serious discipline than, for example, the humanities.
As for the topics studied derivatives, we can say that it is used in many areas of applied sciences. For example, in physics, the derivative of a function of the movement is a function of speed. The second derivative is a function of acceleration. In economics, the derivative is often associated with the definition of maximum profit or minimum cost, finding the limit values. Generally, the meaning of the concept of derivative is the rate of change, increment, relative value. Therefore, the application of this concept is very broad.
Sources
Anton, Howard; Bivens, Irl; Davis, Stephen (February 2, 2005), Calculus: Early Transcendentals Single and Multivariable (8th ed.), New York: Wiley, ISBN 978-0-471-47244-5
Apostol, Tom M. (June 1967), Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra 1 (2nd ed.), Wiley, ISBN 978-0-471-00005-1
