derivative

  1. O

    Derivative of ln(-x)

    Can someone please explain to me why the derivative of ln(-x) is 1/x? Thanks!
  2. L

    The n-th derivative of x*cos(2x)

    Hey, I have to find the f^{(n)}(x) of function f(x) = x \cdot \cos(2x). I know I need to find a Leibnitz formula for derivative of product, but how? Also, I have to solve this formula explicitly, so, f^{(n)}(x) = .... Please help ;)
  3. O

    Calculating derivative using formal definition tricky

    Can someone guide me in terms of finishing off the derivative computation that I have started below? Help is greatly appreciated!
  4. O

    Calculate derivative using formal definition

    I'm really hoping someone can help me calculate the derivative (using the formal definition) for the following function: Here is my attempted solutions but I know it is wrong: Can someone tell me what I am doing incorrectly?
  5. O

    Using formal definition of a limit

    Can someone help me complete the derivative computation below? I'm a bit stuck.
  6. M

    Creating generic formula

    Hi, I'm trying to create a formula for the function $g^n(x)$ which has the following derivative pattern: $$g^1(x) = \frac{e^x(x-1) + 1}{x^2}$$ $$g^2(x) = \frac{e^x(x^2 - 2x + 2) - 2}{x^4}$$ $$g^3(x) = \frac{e^x(x^3 - 3x^2 + 6x - 6) + 6}{x^4}$$ $$g^4(x) = \frac{e^x(x^4 - 4x^3 +12x^2 -24x + 24)...
  7. M

    Minimum volume of empty space in container with water

    Volume of a container is $\frac{4 \pi}{3}$. Water can flow in and out of container.The volume of water in container is given by: $g(t), 0 \leq t \leq 4$, where $t$ is time in hours and $g(t)$ is measured in $m^3$. The rate of change of the volume of water in the container is: $g'(t)= 0.9 - 2.5...
  8. A

    Derivative using the Power Rule

    So I understand how to use the power rule on nearly all problems, however if someone could explain this one to me I'd greatly appreciate it. find the derivative of d/x I know the answer is -d/x^2 but how do you come to get this answer? Thanks so much
  9. O

    Derivative challenge problem

    Hello, Can someone guide me through the following problem? I was able to find the derivative for the equation, but I was not sure what to do afterwards in terms of determining dy/dx at x = 3. - otownsend
  10. H

    Deriv of an Integral

    Let F(x) = integral from x^2 to x^3 of sin (t^2) dt. What is F'(x)? (This problem cannot be addressed by trying to work the integral.)
  11. O

    Finding the second derivative of trig function

    Hi, I hope someone can help. I'm trying to find the second derivative for the trigonometric function y = sinxtanx Apparently the first derivative is y' = sinx + secxtanx even though I got y' = cosxtanx + sinx(secx)^2. I must of missed a step and would appreciate help. The second derivative...
  12. O

    Profit function

    Hi, I'm curious what the value in dollars this solution would be? Considering that P is measured in thousands of dollars and P(1) = 61. Let me know! - Olivia
  13. O

    Bacteria colony growth

    Hi, I hope someone can help. I'm trying to solve the following problem: Apparently I have to create a function which would subtract K(t) from N(t), while taking into account that N(t) starts 60 minutes before K(t). Following that, I would need to use this function to find the critical values...
  14. O

    Derivatives and limits

    Hi, I hope someone can help. I want to know whether my thinking is right or not about the following question: For 15a - Not exactly sure how to interpreted this one and would really appreciate help on this. For 15 b - I interpreted this limit as the derivative for e^x at x = 2, which...
  15. O

    Proving second derivative

    Hi, I hope someone can help me with the following question: I got a different expression for the second derivative than the one above. I'm wondering whether I'm solving this incorrectly or the textbook solution is just wrong. The textbook solution is as follows: Let me know. - olivia
  16. O

    Identifying parent function based on second derivative

    Hi, I hope someone can help. I'm trying to figure out what the graph of the parent function would be based on the graph of its second derivative: I came up with several rough sketches for what parent function could be: 1. 2. 3. Are any of these sketches for the parent function invalid? I...
  17. O

    Sketching derivative function

    Hi, So I'm suppose to make a rough sketch of the derivative for the following function: The derivative function is as follows: Is there any particular reason why the maximum point on the derivative function is about 5? I do agree that the function's slope here is going to be the largest...
  18. O

    Optimizing retail price to maximize profits

    Hi, I'm trying to solve for 11b: I was able to solve for 11a, so I have no confusing there. Am I right to think that the new cost function would be 7.5(165-7x)? Please let me know.
  19. O

    Optimization problem - defining domain

    Hi, Can someone help me formally define what the domain would be for this question? I was fortunately able to reach the correct solution for this question without a well defined range, but for future sake, I would like to be able to know how to derive it. I know that the domain would...
  20. O

    Optimization problem - maximizing profits

    Hi, I'm trying to solve for the following optimization problem: I'm hoping that someone can confirm with me whether or not my calculations are right: The answer according to the textbook is $1100 or $1125. I was able to get the answer of of $1125, but I have no clue where the alternative...