Chapter 2: Q. 7 (page 221)
Explain how the formula for differentiating the natural logarithm function is a special case of the formula for differentiating logarithmic functions of the form
Short Answer
The reason has been explained.
Chapter 2: Q. 7 (page 221)
Explain how the formula for differentiating the natural logarithm function is a special case of the formula for differentiating logarithmic functions of the form
The reason has been explained.
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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.
24.
Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
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
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in “prime” notation.
Use the limit you just found to calculate the exact slope of the tangent line to at . Obviously you should get the same final answer as you did earlier.
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