1. M

    I'm curious what anyone gets for part d

    1. Homework Statement After a wild ride on a windsurfer, you head to a lifeguard tower to fly a kite. You stand on the tower, which is 3 meters above the ground and release your kite. You let out 10 meters of string and the kite begins moving according to the following equation: y(t) = (0.9...
  2. N

    Why is the first derivative velocity?

    Just something that has been bugging me. Can someone bestow why the first derivative is velocity and the second derivative is acceleration. I want to conceptually understand this. Thank you
  3. J

    Calc BC derivative problem with trig and double angle -- Help please

    1. Homework Statement Find f'(x) if f(x) = 8^(sin^2(3x)) Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it. 2. Homework Equations if y=a^u then y' = ln a * a^u * du sin(2x) = 2sinxcosx 3. The Attempt at a Solution...
  4. J

    How to find the equation of this tangent?

    Mod note: Thread moved from Precalc section 1. Homework Statement F(x)=sqrt(-2x^2 +2x+4) 1.discuss variation of f and draw (c) 2.find the equation of tangent line to (c) that passes through point A(-2,0) 3. The Attempt at a Solution I solved first part I found the domain of definition and...
  5. TyroneTheDino

    Finding the distance from origin to a tangent line

    1. Homework Statement Find the distance between the origin and the line tangent to ##x^\frac{2}{3}+y^{\frac{2}{3}}=a^{\frac{2}{3}}## at the point P(x,y) 2. Homework Equations Distance= ##\frac{\left |a_{0}+b_{0}+c \right |}{\sqrt{a^{2}+b^{2}}}## 3. The Attempt at a Solution To begin I...
  6. N

    What version of the definition of derivative

    If my understanding is correct the definition of a derivative is lim h->0 (f(x+h)-f(x))/h However, I've also seen this used: lim x->c (f(x)-f(x))/(x-c) are these both considered valid definition for the derivative or does the derivative have to tend towards zero? I am a bit confused because I...
  7. Titan97

    Question on Mean Value Theorem & Intermediate Value Theorem

    1. Homework Statement for ##0<\alpha,\beta<2##, prove that ##\int_0^4f(t)dt=2[\alpha f(\alpha)+\beta f(\beta)]## 2. Homework Equations Mean value theorem: ##f'(c)=\frac{f(b)-f(a)}{b-a}## 3. The Attempt at a Solution I got the answer for the question but I have made an assumption but I don't...
  8. N

    Confused on these two derivative problems

    1. Homework Statement a. k(t) = (sqrt(t+1))/(2t+1) b. y = (3^(x^2+1))(ln(2)) 3. The Attempt at a Solution For the first problem, I know I use the quotient rule for derivatives (L)(DH)-(H)(DL)/((L)^2) which would go to: ((2t+1)(1/(2sqrt(t+1)) - (sqrt(t+1))(2))/((2t+1)^2) I get stuck here...
  9. haael

    How does the Kalman filter calculate derivatives?

    Suppose we have a Kalman filter. We have a position sensor, for example GPS. We use the filter to estimate position. However in all examples I see higher derivatives in the state vector: speed, acceleration and sometimes jerk. There is no sensor that calculates these values directly, so they...
  10. A

    Velocity Derivative of a Sinusoidal Wave (Counter-Intuitive)

    What's the matter: So, I think I have some skills when it comes to differentiation after taking calculus 2 last semester, but when it starts to intertwine with physics, and interpreting physical phenomenon through equations, It appears I could use some help. Anyway, the problem that I got hung...
  11. R

    Tension on a Rope Deflected by a Pulley: Differentials

    Hi all, first post here. I'm a junior Physics/Math double major at UMass Amherst, playing with some problems over the summer. I'll get right into it. A rope with constant tension T is deflected through the angle 2\theta_{0} by a smooth, fixed pulley. What is the force on the pulley? It is...
  12. Chrono G. Xay

    'Wheel-like' Mathematics (Modulating Trig Functions?)

    As part of a personal musicology project I found myself with the mathematical model of a geometry which utilizes the equation a*(a/b)sin(pi*x) The only problem with this is that I need to take the integral from -1/2 <= x <= 1/2, and according to Wolfram Alpha no such integral exists. I can...
  13. P

    Foundations What's a good book for last year of A levels Maths?

    I'm looking for a book to self-study this summer before my last course of Bachillerato (A Levels or High School in other countries). My performance in Mathematics has only improved and I've just been given the maximum mark this last term (10/10 or A+). This has motivated me a lot to keep...
  14. R

    Derivatives and Linear transformations

    Let G be a non-empty open connected set in Rn, f be a differentiable function from G into R, and A be a linear transformation from Rn to R. If f '(a)=A for all a in G, find f and prove your answer. I thought of f as being the same as the linear transformation, i.e. f(x)=A(x). Is this true?
  15. leafjerky

    Deriving formulas used for vectors in physics.

    Hey guys and gals, I'm taking an online physics course just to kind of learn the basics before I take the real thing this summer. The course is from OpenYale for those interested ( Anyways, the professor was talking about some formulas for finding ##\vec{r}(t) = r(i(cos\omega t) +...
  16. M

    Calculus Derivative Terminology

    I have attached an image of a function that I fit to a scatter plot, and I would like to know if there is a term for the point on the function at which the slope transitions from being less than -1 to greater than -1. I have highlighted this point approximately in yellow...
  17. Prof. 27

    Linear Ordinary Differential Equation: Definition

    1. Homework Statement The website says this: "It is Linear when the variable (and its derivatives) has no exponent or other function put on it. So no y2, y3, √y, sin(y), ln(y) etc, just plain y (or whatever the variable is). More formally a Linear Differential Equation is in the form: dy/dx +...
  18. AdityaDev

    Finding y=f(x)

    1. Homework Statement Given two curves y=f(x) passing through (0,1) and ##g(x)=\int\limits_{-\infty}^xf(t)dt## passing through (0,1/n). The tangents drawn to both curves at the points with equal abscissae intersect on the x-axis. Find y=f(x). 2. Homework Equations None 3. The Attempt at a...
  19. B

    Derivative of metric with respect to metric

    I'm hoping someone can clarify for me, I have seen the following used: \frac{\partial}{\partial g^{ab}}\left( g^{cd} \right) = \frac{1}{2} \left( \delta_a^c \delta_b^d + \delta_b^c \delta_a^d\right) I understand the two half terms are used to account for the symmetry of the metric tensor...
  20. D

    Richardson Extrapolation with 3 steps?

    1. Homework Statement use richardson extrapolation to estimate the first derivative y=ln(x), x=5 using steps of 2, 1, 0.5. Four decimal points. obtain true relative error for the last estimate and comment on its value. 2. Homework Equations deriv ln(x)=1/x 3. The Attempt at a Solution I...
  21. Albo1125

    Using the derivative of the formula of the number of nuclei

    Hi all, I have a question concerning the derivative of the formula of the number of nuclei. I hope I've posted this in the right section, I'm new here :P. Anyway, in the question, the given values are: At a certain time t, there is an amount of radioactive Br-82. The activity A is 7.4*1014 Bq...
  22. T

    Maximize volume of a box

    Suppose someone gives you a rectangular sheet of length a and width b (so b ≤ a). You make a topless box by cutting out a square with length x out of each corner and folding up the sides. How should you cut the sheet so as to maximize the volume of your box?
  23. S

    Natural log differentiation question

    1. Homework Statement f(x) = 1/ln (10-x) -- I would assume it to be a fairly simple equation, but I am screwing it up 2. Homework Equations What is f'(x)? 3. The Attempt at a Solution f'(x) = (ln (10-x))^-1 = -(ln (10-x))^-2 * -1 * 1/(10-x) -- 2 negatives cancel out =...
  24. Ondina

    Complex derivative of x: ((x)^(1/x))'

    <<Moderator note: Remember that filling in the complete homework template is mandatory in the homework forums. This thread has not been deleted due to containing relevant replies.>> 1. Homework Statement ((x)^(1/x))' 2. Homework Equations This probably isn't overly dificult, but it has got me...
  25. S

    New Calc student w/ a derivative question

    1. Homework Statement Hello all, thank you for the help in advance. It's a two-sided derivative problem, for lack of a better term, and I appreciate all hints or help. If we have a function y so that y=bx for all x<0, and y= x^2-13x for all x> or = 0, for what value of b is y differentiable...
  26. N

    Taking the time derivative of a curl

    Is the time derivative of a curl commutative? I think I may have answered this question.... Only the partial time derivative of a curl is commutative? The total time derivative is not, since for example in cartesian coordinates, x,y,and z can themselves be functions of time. In spherical and...
  27. C

    Kinetic Energy Time Derivative

    1. Homework Statement So the first part asks to prove the time derivative of kinetic energy is dT/dt=F dot product v which I did not problem. but then the second part of the problem asks to prove that if the mass is changing with time then the time derivative of d(mT)/dt=F dot product m and...
  28. powerof

    Symmetry in second order partial derivatives and chain rule

    When can I do the following where ##h_{i}## is a function of ##(x_{1},...,x_{n})##? \frac{\partial}{\partial x_{k}}\frac{\partial f(h_{1},...,h_{n})}{\partial h_{m}}\overset{?}{=}\frac{\partial}{\partial h_{m}}\frac{\partial f(h_{1},...,h_{n})}{\partial x_{m}}\overset{\underbrace{chain\...
  29. D

    Proving the fundamental theorem of calculus using limits

    Would it be a legitimate (valid) proof to use an \epsilon-\delta limit approach to prove the fundamental theorem of calculus? i.e. as the FTC states that if f is a continuous function on [a,b], then we can define a function F: [a,b]\rightarrow\mathbb{R} such that F(x)=\int_{a}^{x}f(t)dt Then F...
  30. N

    For f(x) = abs(x^3 - 9x), does f'(0) exist

    1. Homework Statement For f(x) = abs(x^3 - 9x), does f'(0) exist? 3. The Attempt at a Solution The way I tried to solve this question was to find the right hand and left hand derivative at x = 0. Right hand derivative = (lim h--> 0+) f(h) - f(0) / h = (lim h--> 0+) abs(h^3 - 9h) / h...