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
explanation: The text extract is a discussion thread from a homework help forum, where a user named Yapper is seeking assistance with calculus problems. The user posts two specific questions and receives responses from other users, including vincentchan and dextercioby, who provide guidance and explanations.
  
  1. The first question is about finding the derivative of an integral with a variable upper limit.
  2. The second question is about differentiating a logarithmic function with a variable base.
  
  The extract contains multiple questions and answers.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract is a discussion thread from a homework help forum, where a user named Yapper is seeking assistance with calculus problems. The user posts two specific questions and receives responses from other users, including vincentchan and dextercioby, who provide guidance and explanations.
  
  1. The first question is about finding the derivative of an integral with a variable upper limit.
  2. The second question is about differentiating a logarithmic function with a variable base.
  
  The extract contains multiple questions and answers.
  
  Label: multiple-question-and-answer