calculus help

Find the derivative of the function.

y = integral from cosx to sinx
(ln(8+3v)) dv

lower limit = cosx

upper limit = sinx

y'(x) = ????

  1. 👍
  2. 👎
  3. 👁
  1. Just use Lebniz's Rule:

    d/dx ∫[a(x),b(x)] f(t) dt =
    f(b(x))b' - f(a(x))a'

    d/dx ∫[cosx,sinx] ln(8+3v) dv
    = ln(8+3sinx)(cosx) - ln(8+3cosx)(-sinx)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Trig.......

    I need to prove that the following is true. Thanks (2tanx /1-tan^x)+(1/2cos^2x-1)= (cosx+sinx)/(cosx - sinx) and thanks ........... check your typing. I tried 30º, the two sides are not equal, they differ by 1 oh , thank you Mr

  2. Precalculus/Trig

    I can't seem to prove these trig identities and would really appreciate help: 1. cosx + 1/sin^3x = cscx/1 - cosx I changed the 1: cosx/sin^3x + sin^3x/sin^3x = cscx/1-cosx Simplified: cosx + sin^3x/sin^3x = cscx/1-cosx I don't

  3. Math

    (sinx - cosx)(sinx + cosx) = 2sin^2x -1 I need some tips on trigonometric identities. Why shouldn't I just turn (sinx + cosx) into 1 and would it still have the same identity?

  4. Calculus

    Integrate sinx(cosx)^2dx using the substitution u=sinx. I know how to do this using u =cosx, but not sinx. The next problem on the homework was the same question except it asked to use u=cosx, so there couldn't have been a

  1. Math (Definite Integrals)

    Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2 - x^2) dx -r While I recognize that this looks similar to a circle function, I'm not sure

  2. Calculus prince@18

    let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of

  3. inverse

    If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means

  4. Calculus

    determine the absolute extreme values of the function f(x)=sinx-cosx+6 on the interval 0

  1. maths - trigonometry

    I've asked about this same question before, and someone gave me the way to finish, which I understand to some extent. I need help figuring out what they did in the second step though. How they got to the third step from the

  2. limits

    what is the derivative of e^(3*ln(x^2)) i keep getting 6/x * e^(3*ln(x^2)) but that's not one of the multiple choice so am i doing something wront. also, what is the limit of (1-cosx)/(2*(sinx)^2) as x approaches zero. is the

  3. Calculus - Integration

    I ran across this one the other day. See what you can make of it. Find the integral of ecosxsinx - (sinx+cosx)esinx+cosx ----------------------------------------- esin2x-2esinx+1

  4. Calculus

    If y=3/(sinx+cosx) , find dy/dx A. 3sinx-3cosx B. 3/(sinx+cosx)^2 C. -3/(sinx+cosx)^2 D. 3(cosx-sinx)/(sinx+cosx)^2 E. 3(sinx-cosx)/(1+2sinxcosx)

You can view more similar questions or ask a new question.