text: # Derivative f(x)=x^3, f(a+h)-f(a)/h
  
  ## Homework Statement
  
  f(x)=x^3 f(a+h)-f(a)/h
  
  ## Homework Equations
  
  I am having troubles at the moment with the process, I am getting a^3+3a^2h+3ah^2+h^3-a^3.
  
  ## The Attempt at a Solution
  
  I have simplified the equation further and got 3a^2+3ah+h^2, help would be appreciated. Thanks for reading.
  
  You are trying to look for the derivative? Or just simplifying the equation?
  
  You will need to get the limit as h approaches 0 for derivative.
  
  You are trying to look for the derivative? Or just simplifying the equation?
  
  I already know the derivative, so just simplifying the equation.
  
  If you just need to simplify the equation f(a+h)-f(a)/h, then you have already done so by getting 3a^2+3ah+h^2 as the answer.
  
  If you just need to simplify the equation f(a+h)-f(a)/h, then you have already done so by getting 3a^2+3ah+h^2 as the answer.
  
  http://img192.imageshack.us/f/derivative.jpg/" [Broken] Can you check my math? Please.
  
  Last edited by a moderator:
  It should be fine.... According to my education system ><
  
  For me, i'll straight away use the definition of derivative
  f'(x) = limh->0 f(a+h)-f(a)/h
  
  Would not try to derive all the way from (f(b)-f(a))/(b-a), too time consuming.
  
  Ok, thank you.
explanation: The document is a discussion about simplifying the expression \( f(a+h) - f(a) / h \) for the function \( f(x) = x^3 \). It includes a question about the simplification process and an answer confirming the simplified form. The document also touches on the concept of the derivative and the limit as \( h \) approaches 0.
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: # Derivative f(x)=x^3, f(a+h)-f(a)/h
  
  ## Homework Statement
  
  f(x)=x^3 f(a+h)-f(a)/h
  
  ## Homework Equations
  
  I am having troubles at the moment with the process, I am getting a^3+3a^2h+3ah^2+h^3-a^3.
  
  ## The Attempt at a Solution
  
  I have simplified the equation further and got 3a^2+3ah+h^2, help would be appreciated. Thanks for reading.
  
  You are trying to look for the derivative? Or just simplifying the equation?
  
  You will need to get the limit as h approaches 0 for derivative.
  
  You are trying to look for the derivative? Or just simplifying the equation?
  
  I already know the derivative, so just simplifying the equation.
  
  If you just need to simplify the equation f(a+h)-f(a)/h, then you have already done so by getting 3a^2+3ah+h^2 as the answer.
  
  If you just need to simplify the equation f(a+h)-f(a)/h, then you have already done so by getting 3a^2+3ah+h^2 as the answer.
  
  http://img192.imageshack.us/f/derivative.jpg/" [Broken] Can you check my math? Please.
  
  Last edited by a moderator:
  It should be fine.... According to my education system ><
  
  For me, i'll straight away use the definition of derivative
  f'(x) = limh->0 f(a+h)-f(a)/h
  
  Would not try to derive all the way from (f(b)-f(a))/(b-a), too time consuming.
  
  Ok, thank you.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a discussion about simplifying the expression \( f(a+h) - f(a) / h \) for the function \( f(x) = x^3 \). It includes a question about the simplification process and an answer confirming the simplified form. The document also touches on the concept of the derivative and the limit as \( h \) approaches 0.
  
  Label: question-and-answer