Purchase Solution

14 Derivative Problems : Product Rule, Quotient Rule, Chain Rule, First and Second Derivative and Finding Maximum or Minimum

Not what you're looking for?

Ask Custom Question

Rules and Applications of the Derivative
--------------------------------------------------------------------------------
1. Use the Product Rule to find the derivatives of the following functions:

a. f(X) = (1- X^2)*(1+100X)

b. f(X) = (5X + X^-1)*(3X + X^2)

c. f(X) = (X^.5)*(1-X)

d. f(X) = (X^3 + X^4)*(30 + X^2)

2. Use the Chain Rule to find the derivatives of the following functions:

a. f(X) = (1- X^2)^5

b. f(X) = (5X + X^-1)^-1

c. f(X) =(1-X)^2

d. f(X) = (X^3 + X^4)^3

3. Use the Quotient Rule to find the derivatives of the following functions:

a. f(X) = 100/X^4

b. f(X) = 1/(5X + X^2)

c. f(X) =5/(1-X)

4. For each of the following functions find the 1) first and second derivative, 2) explain whether or not the function has a maximum or a minimum, and how you reached that conclusion, and 3) the value of the maximum or minimum

a. f(X) = 5X^2 - 2X

b. f(X) = 1000X - X^2

c. f(X) = 8X^3 - 4X^2

sorry about that forgot the powers

Purchase this Solution
Solution Summary

Fourteen derivative problems are solved regarding Product Rule, Quotient Rule, Chain Rule, First and Second Derivative and Finding Maximum or Minimum. The solution is detailed and well presented.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Derivative Problems

    Find the 1st derivative of f(x) = [(3 - x^(2/3))][(x^(2/3) + 2)^(1/2)] Rewrite: You should use the product rule and the chain rule in this case Product rule: Chain rule: so, Prob. 4.

  • Quotient / Composite rules

    An use the first derivative test to see whether they are local maximum or local minimum of f(x). c. what are the maximum and minimum values of the function f(x) at interval [-6,2] 2.

  • Differentiation

    14740 Derivatives using product rule, quotient rule, or chain rule. Find the derivative of each expression, using the product rule, quotient rule, or chain rule. 1. P= e^(2x)/x 2. B= square root of sin * square root of x 3.

  • First and second derivatives of the function y=((1-x)/x^2)^3

    Y = [(1-x)/x2]^3 First derivative (remember d/dx (a^n) = n a^(n-1) dy/dx = 3 [(1-x)/x2]2 {d/dx (1-x)/x2} We need to calculate d/dx (1-x)/x2, for this, use the quotient rule or the product rule (this is simple) Take (1-x) as first function and

  • Derivatives, Product Rule, Quotient Rule, and Composite Rule

    The solution gives detailed steps on finding the derivatives for various questions using product rule, quotient rule and composite rule. All formula and calculations are shown and explained.

  • Partial derivatives

    Find the indicated partial derivatives. 1.) f(x,y)= sin(y-x); df/dx(3,3) Using the chain rule, Therefore, at (x, y) =(3, 3), 2.)z= (x^3 + y^3)/(x^2 + y^2); dz/dx, dz/dy Using chain rule and quotient rule, Similar to x, we find the

  • Calculus

    By chain rule, the derivative is 2 * 5(t^3 - 1)^4 * 3t^2 = 30t^2 (t^3 - 1)^4.

  • Find the Hessian

    In doing partial derivative (use chain rule) (product rule) (first derivative w.r.t x, second derivative w.r.t. y) (first derivative w.r.t x, second derivative w.r.t. z) So we have completed the first row of the Hessian.

  • Finding a derivative using the quotient rule

    105957 Finding a derivative using the quotient rule Q: Find the derivative of the following function h(x) = x^5/(x^2-7). Please view Word Doc for a clearer version. A: To find the derivative we must apply the Quotient Rule for Derivatives.

View More Related Solutions