Read about derivatives | 40 Discussions | Page 2

  1. X

    Expressing A Quantity In Polar Coordinates?

    Homework Statement Express the quantity ∂2/∂x2+∂2/∂y2 in polar coordinates. Homework Equations x=ρcosφ y=ρsinφ ρ=sqrt(x2+y2) The Attempt at a Solution This is my first post, so I apologize for any weird looking equations, etc. I know that this is not a difficult problem, but I just cannot...
  2. M

    Understanding distances, derivatives, and integrals help?

    Homework Statement Two railroad tracks intersect at right angles at station O. At 10AM the train A, moving west with constant speed of 50 km/h, leaves the station O. One hour later train B, moving south with the constant speed of 60 km/h, passes through the station O. Find minimum distance...
  3. D

    Derive a Velocity function

    Homework Statement Derive the function for the acceleration from this function v=√(2P/M)(√T) The answer is √(P/2MT) I have tried many different attempts but I am still unable to reach this answer. [/B] I am sure the process to get to the answer is a simple one but for some reason I am...
  4. wirefree

    Is differentiation a possible approach?

    Question: I have a function of time. Its expression has a constant 'b' in it. I am asked to ascertain how changing 'b' affects the function. Specifically, I have velocity as a function of time which accounts for drag forces; 'b' is the drag coefficient. I am asked to ascertain how changing 'b'...
  5. R

    Inverse Laplace Transform with e^{a s}

    Homework Statement How can I take the Inverse Laplace Transform of $F(s) = \frac{d}{ds}\left(\frac{1-e^{5s}}{s}\right)$? I have tried going with inverse of the derivative and convolution (even tried evaluating the derivative and go from there) but although I can get to some results none of them...
  6. C

    Another cannonball question

    Homework Statement A Cannonball is shot upward from the ground into the air at t=0 sec. With initial velocity of 50m/s. Its height above the ground in metres is given by s(t)=50t-4.9t^2 . ----What is the velocity of the cannonball when it is 100m above the ground on the way up? "says the...
  7. R

    Component functions and coordinates of linear transformation

    Let A(a, b, c) and A'(a′,b′,c′) be two distinct points in R3. Let f from [0 , 1] to R3 be defined by f(t) = (1 -t) A + t A'. Instead of calling the component functions of f ,(f1, f2, f3) let us simply write f = (x, y, z). Express x; y; z in terms of the coordinates of A and A, and t. I thought...
  8. R

    Differentiability in R2

    Let U={(x,y) in R2:x2+y2<4}, and let f(x,y)=√.(4−x2−y2) Prove that f is differentiable, and find its derivative. I do know how to prove it is differentiable at a specific point in R2, but I could not generalize it to prove it differentiable on R2. Any hint?
  9. D

    A question on proving the chain rule

    I'm currently reviewing my knowledge of calculus and trying to include rigourous (ish) proofs in my personal notes as I don't like accepting things in maths on face value. I've constructed a proof for the chain rule and was wondering if people wouldn't mind checking it and letting me know if it...
  10. M

    Differentiation of a sphere -- raindrop evaporating as it falls

    < Moderator Note -- Thread moved from the technical PF Calculus forum > I can't seem to grasp the idea of this problem, any help is much needed. The problem reads, "As a spherical raindrop falls, it reaches a layer of dry air and begins to evaporate at a rate that is proportional to its...
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