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Chapter 2: Q. 68 (page 223)
Use the definition of the derivative and the definition of the number e to prove that is its own derivative.
It is proved that derivative of the given function isonly.
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Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in 鈥減rime鈥� notation.
Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Stuart left his house at noon and walked north on Pine Street for minutes. At that point he realized he was late for an appointment at the dentist, whose office was located south of Stuart鈥檚 house on Pine Street; fearing he would be late, Stuart sprinted south on Pine Street, past his house, and on to the dentist鈥檚 office. When he got there, he found the office closed for lunch; he was minutes early for his appointment. Stuart waited at the office for minutes and then found out that his appointment was actually for the next day, so he walked back to his house. Sketch a graph that describes Stuart鈥檚 position over time. Then sketch a graph that describes Stuart鈥檚 velocity over time.
Use the differentiation rules developed in this section to find
the derivatives of the functions
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