text: # Homework Help: Need Calculus Help
  
  1. Jan 13, 2005
  
  ### Yapper
  
  I am studying for a Calculus test and I need some help withsome concepts...
  
  1) The problem is find the derivatie of y= (integral a=1 b=sinx of) t^3 dt. I went into my book and found a formula for it. The derivative of (intergral a=constant b=x of) f(t) dt = f(x). So I got (sinx)^3 is this right? If so can someone explain this concept and provide a proof for it? My text book isn't good at explaining things...
  
  2)The problem is to differentiate y=log base x (2x). So I chamged it to ln2x/lnx from there can i just use divison rule? u'v -uv'/v^2? in that case would it be (lnx/x-ln2x/x)/(lnx)^2?
  
  2. Jan 13, 2005
  
  ### vincentchan
  
  1: is your derivative repect to x or t? this make a huge different
  2: you are perfectly correct....
  
  3. Jan 13, 2005
  
  ### Yapper
  
  y= (integral a=1 b=sinx of) t^3 dt, so the differential unit is t, since it is dt, im guessing, thats all the information i was given
  
  4. Jan 13, 2005
  
  ### dextercioby
  
  Then it's wrong.Compute the antiderivative of the integrand and apply the fundamental formula of Leibniz & Newton.
  
  Daniel.
  
  5. Jan 13, 2005
  
  ### Yapper
  
  No clue what you just said...
  
  6. Jan 13, 2005
  
  ### Yapper
  
  How do I use LaTex to make it clearer?
  
  7. Jan 13, 2005
  
  ### vincentchan
  
  OK, your integrand is t^3 and the limit is from 1 to sinx.... right?
  Here is how u do the derivative of this monster...
  if it is repect to t.. do the integral and substitude 1 and sinx in.... and do the derivative
  if it is repect to x.. do the integral and substitude 1 and sinx in.... and do the derivative
  
  basically, what you gonna do is do the integral and substitude 1 and sinx in.... and do the derivative, OK?
  
  but if the derivative is repect to t, the result is trivial......
  
  8. Jan 13, 2005
  
  ### Yapper
  
  I dont understand.... I do the integral and I get t^4/4 substitutre for sinx and do the derivative I get sinx^3cosx is that right?
  
  9. Jan 13, 2005
  
  ### dextercioby
  
  There's a compiler that will "translate" all code lines u type in the window in which u write the message.Use the function "preview post" to check formulas for typos.
  
  The result is trivial.It can be shown that
  $$\frac{d}{dx}{\int_{const.}^{f(x)} u(t) dt =u(f(x))f'(x)$$
  
  I still reccomend to you to do the integration and then the differentiation and confront with the result my formula gives you.
  
  Daniel.
  
  10. Jan 13, 2005
  
  ### vincentchan
  
  $$\frac{d}{dx}{\int_{const.}^{f(x)} u(t) dt =u(f(x)) \frac{d}{dx}f(x)$$
  
  11. Jan 13, 2005
  
  ### Yapper
  
  Oh ok... my books says g(x) = (intergral from a constant to x of) f(t) dt, then g'(x) = f(x)
  
  12. Jan 13, 2005
  
  ### Yapper
  
  Thanks for all the help!!! and is there a website or a help file that has the code?
  
  Last edited: Jan 13, 2005
  13. Jan 13, 2005
  
  ### cepheid
  
  Staff Emeritus