Chapter 2: Q.35 (page 198)
Use the differentiation rules developed in this section to find
the derivatives of the functions
Short Answer
The derivative of
Chapter 2: Q.35 (page 198)
Use the differentiation rules developed in this section to find
the derivatives of the functions
The derivative of
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Get started for freeDifferentiate in three ways. When you have completed all three parts, show that your three answers are the same:
(a) with the chain rule
(b) with the product rule but not the chain rule
(c) without the chain or product rules.
Find the derivatives of the functions in Exercises 21โ46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
For each function f and value in Exercises 35โ44, use a sequence of approximations to estimate . Illustrate your work with an appropriate sequence of graphs of secant lines.
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
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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