1. Z

    Need help with partial derivative

    f(x,y,z)=ez+e2yarctan(y/x) This is what i have calculated (Partial derivative w.r.t x) dfdx= -(e2yy)/(y2+x2) (Partial derivative w.r.t y) dfdy= (e2yx)/(y2+x2) + 2e2yarctan(y/x) (Partial derivative w.r.t z) dfdz= ez Here comes the problem g(s,t)=f(s,u(s,t),v(s,t)), where u(s,t)=st and...
  2. A

    Trying to find partial derivatives

    I have an implicit equation relating P1, P2, Q: P1 - P2 - k * ( f(P1,Q) + g(P2,Q) ) = 0 ie. given P1, P2, I can find Q by iteration. I know the functions f and g and also have their analytical derivatives. I need to find partial derivatives dQ/dP1 and dQ/dP2
  3. Y

    chemical reaction rate differential equation.

    Hi guys, Need some help with this separable differential equation. I understand that I have to use separation of variables and integration by partial fractions (it is a second order reaction rate equation where K is the reaction rate constant). I can get it to this form...
  4. P

    Calculus newbie: Need help splitting (x + 1) / (6x + x^2) into partial fractions

    As mentioned in the title, I am attempting to split (x + 1) / (6x) + (x^2) into partial fractions. What I currently have is the following: "x + 1 = A(x^2) + B(6x) + c(6x)(x). If I understand how to do partial fractions correctly, I must now find a number that "negates" each term of that...
  5. X

    implicit partial differentiation

    in the notes , 'by applying chain rule to LHS of the above equation ' , which eqaution is the author referring to ? it's given that f /x + (f/z)(z/x) = 0 , why not f /x + (f/z)(z/x) + (f/y)(y/x) = 0 ??? As we can see , the function contain variable x , y and z
  6. X

    partial derivative

    why the partial derivative (dw/dx) is y / (2x^2)(sqrt rt (xy +y) ) , how to get that ? why not like this ?
  7. X

    express (1/ (x+2)^2) ) into partial fraction

    is it possible to do that ? i tried that , but o get back (1/ (x+2)^2) ) my working is (1/ (x+2)^2) ) = [ A / (x+2) ] + [ B / ((x+2)^2) ] 1= A (x+2) + B then i sub x = -2 , i gt B = 1 then i sub x= 1 , A = 0 can someone explain , i am confused.
  8. U

    Partial Fraction Integration...3

    This is a monster problem. ∫ (x² - 5x + 16)/[(2x + 1)(x - 2)²] dx (x² - 5x + 16)/[(2x + 1)(x - 2)²] = A/(2x + 1) + B/(x - 2) + C/(x - 2)² x² - 5x + 16 = A(x - 2)² + B(2x + 1)(x - 2) + C(2x + 1) I am stuck here.
  9. U

    Partial Fraction Integration...2

    ∫ dx / (1 - x^2) = ∫ dx / (1 + x)(1 - x) = ∫ A dx / (1 + x) + ∫ B dx / (1 - x) 1 / (1 - x^2) = A / (1 + x) + B / (1 - x) Multiplying through by (1 - x^2) gives 1 = A(1 + x) + B(1 - x) Combining like terms gives 1 = (A - B)x + (A + B) I am stuck here.
  10. U

    Partial Fraction Integration...1

    ∫ 1/(x^3 + x^2) dx Factor the denominator: ∫ 1/[x^2(x + 1)] dx I now break this up into partial fractions. By Partial fractions: 1/[x^2(x + 1)] = A/x + B/x^2 + C/(x + 1) Multiplying through the fractions gives me: 1 = Ax(x + 1) + B(x + 1) + Cx^2 I am stuck here.
  11. U

    Partial Fraction Decomposition

    We started learning integration by partial fraction decomposition. For the most part, I understand what to do. However, there are two particular cases I am a bit confused about. Sometimes, one of the numerators is Bx + C and depending on the problem, a fraction can be divided into three parts...
  12. M

    Find the boundary condition of the nonlinear partial differential equations

    I have first-order nonlinear partial differential equations \frac{du}{dt}+u\frac{du}{dx} =-u^3, u\Bigr|_{t=0}=f(x) solution dt=\frac{dx}{u}=-\frac{du}{u^3} F(x-\frac{1}{u},t-\frac{1}{2u^2}) Need find boundary conditions f(x) (for example u(t=0,x)=x and find $u$) But my simple function have a...
  13. X

    partial fraction of (1+s^2) / [ (s^2) ((s+3)^2 ) ]

    what's wrong with my working , i cant get the correct ans although i have checked many times .
  14. B

    Integration Questions: Trig Sub, Partial Fractions, Cover Method

    Hi, I have two questions (well 3 really): 1. to find the integral of 2/(y2 + 9y + 8) - do I use partial fractions? I can see the denominator factors to (y+ 8)(y+1). We were taught the cover method and I have read about it however still don't get it. I am so used to cross-multiplying long...
  15. MechanicalPencil

    Partial Derivative Problem

    I'm not 100% sure with how to proceed with this question beyond taking the partials. Ive attempted to isolate one term with mu in each partial, but I haven't been able to do it in the partial with respect to tau. i was thinking that I could equate the two isolated terms and solve for mu? This is...
  16. S

    Question About Partial Differentiation

    If I partially differentiate sin(2xy) with respect to x is the answer 4xcos(2xy)? If it's differentiated with respect to y is the answer 4ycos(2xy)? My question relates to whether when converting from sin to cos you multiply by 2 in each case. Thanks.
  17. S

    Integration Partial Sums

    For the first problem on this sheet based on my work I am getting answer choice A with the numerator and denominator flipped from what is shown in A. Can someone please tell me what I did wrong.
  18. G

    Partial Derivatives

    I have this problem on the review for the final. When i worked it out, I got the bottom equation to be equal to 0. The bounds are x+2y and x-2y if you cant see it
  19. D

    derivative of multiple integral

    I have a problem in derivative of multiple integrals. for example i don't know how can I do it for the below question. would you please help me to solve it? thanks A= \int \int q(y,z)(Ln|z|+tr(z^{-1}(x'x-2 x' y+y' y)))dy dz where x,y,z are vectors we want derivative of A wrt q(y,z). please look...
  20. S

    Partial fractions with a lone x^2

    I had a question about when you do partial fractions to solve an integral problem: Say we have an integrand like 1/(x^2*(x+2)^2) Now, I feel completely at ease with how to handle repeated factors as well as quadratics like (x+2)^2. But I suddenly found myself a bit hesitant about x^2. I mean...