In Exam 1, Question 4, we use the definition of the derivative to prove the product rule. But when you go to the last line of the solutions, the term h is still in the denominator, and this h tends towards zero. In previous examples we need to cancel this h out of the difference quotient, but why can we let it stay in this instance?

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/exam-1/session-22-materials-for-exam-1/MIT18_01SCF10_exam1sol.pdf

Question

In Exam 1, Question 4, we use the definition of the derivative to prove the product rule. But when you go to the last line of the solutions, the term h is still in the denominator, and this h tends towards zero. In previous examples we need to cancel this h out of the difference quotient, but why can we let it stay in this instance? 

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/exam-1/session-22-materials-for-exam-1/MIT18_01SCF10_exam1sol.pdf

stacey · Answer

|dw:1342039565948:dw|