Chapter 2: Q. 4 (page 209)
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in “prime” notation.
Short Answer
In prime notation the derivative is:
Chapter 2: Q. 4 (page 209)
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in “prime” notation.
In prime notation the derivative is:
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Get started for freeUse (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.
29.
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.
23.
Use the definition of the derivative to prove the following special case of the product rule
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Taking the limit: We have seen that if f is a smooth function, then This approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.
.
Use the limit just defined to calculate the exact slope of the tangent line toat
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