Chapter 2: Q. 65 (page 198)
Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
Short Answer
The derivative of the function is.
Chapter 2: Q. 65 (page 198)
Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
The derivative of the function is.
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Get started for freeuse the definition of derivative to directly prove the differentiation rules for constant and identity function
Last night Phil went jogging along Main Street. His distance from the post office t minutes after p.m. is shown in the preceding graph at the right.
(a) Give a narrative (that matches the graph) of what Phil did on his jog.
(b) Sketch a graph that represents Phil’s instantaneous velocity t minutes after p.m. Make sure you label the tick marks on the vertical axis as accurately as you can.
(c) When was Phil jogging the fastest? The slowest? When was he the farthest away from the post office? The closest to the post office?
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The line tangent to the graph of at the point
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
27.
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in “prime” notation.
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