F. Perform some algebra to get alone, on the left hand side, and you are done computing the derivative of the original function f(z).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Question 2f
2. Now, consider the function
S(z) = rrz
Follow a similar pattern to the one explained in class and answer the following questions:
A. Why can't we use the Power Rule to compute f'(r)?
B. Why can't we use a formula like 4(3") = (3") In 3 to compute f'(x)?
C. In order to compute f'(r) start with the equation y = r2z, Take the logarithm of
both sides to get
In y = In (r2*),
then use a property of logarithms to help you find the derivative of In (r2).
D. Now use implicit differentiation to find #(In y).
E. Since In y = In (r2*), you can equate your answers from parts C and D. Do so, and
then replace all y terms by r2wa
3
F. Perform some algebra to get d alone, on the left hand side, and you are done
computing the derivative of the original function f(z).
G. Now, let g(r) = e2mz In z. What is the relationship between f(r) and g(r)?
H. If g(z) = e²7z In z, compute g'(z). What techniques should you be using in this
case?
I. Since you have done the same problem in two different ways, show that the answers
from parts F and H are identical.
3. The following derivatives are expressed by using the Leibniz notation for differenti-
ation. Calculate each
f them:
a)
d sin(r?)
da
b)
(** cos 2) =
Transcribed Image Text:2. Now, consider the function S(z) = rrz Follow a similar pattern to the one explained in class and answer the following questions: A. Why can't we use the Power Rule to compute f'(r)? B. Why can't we use a formula like 4(3") = (3") In 3 to compute f'(x)? C. In order to compute f'(r) start with the equation y = r2z, Take the logarithm of both sides to get In y = In (r2*), then use a property of logarithms to help you find the derivative of In (r2). D. Now use implicit differentiation to find #(In y). E. Since In y = In (r2*), you can equate your answers from parts C and D. Do so, and then replace all y terms by r2wa 3 F. Perform some algebra to get d alone, on the left hand side, and you are done computing the derivative of the original function f(z). G. Now, let g(r) = e2mz In z. What is the relationship between f(r) and g(r)? H. If g(z) = e²7z In z, compute g'(z). What techniques should you be using in this case? I. Since you have done the same problem in two different ways, show that the answers from parts F and H are identical. 3. The following derivatives are expressed by using the Leibniz notation for differenti- ation. Calculate each f them: a) d sin(r?) da b) (** cos 2) =
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