4-86 Use the formula in Exercise 83. 4. If f(4) = 5 and f'(4) =}, find (f-')'(5). 3 5. If f(x) = x + e*, find (f ')'(1). 5. If f(x) = x + 3 sin x + 2 cos x, find (f1)'(2).
4-86 Use the formula in Exercise 83. 4. If f(4) = 5 and f'(4) =}, find (f-')'(5). 3 5. If f(x) = x + e*, find (f ')'(1). 5. If f(x) = x + 3 sin x + 2 cos x, find (f1)'(2).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
85.
Transcribed Image Text:(b) Another way of defining sec x that is sometimes used
is to say that y = sec¯'x A sec y = x and
0<y< T, y # /2. Show that, with this definition,
d
1
(sec-x) =
dx
xis x|/x2 - 1
83. Derivatives of Inverse Functions Suppose that f is a one-
to-one differentiable function and its inverse function f- is
also differentiable. Use implicit differentiation to show that
1
(f-)'(x) =
T 0) (1)
f'(f-'(x))
provided that the denominator is not 0.
84-86 Use the formula in Exercise 83.
lan84. If f(4) –
= 5 and f'(4) = }., find (f-')'(5).
85. If f(x) = x + e*, find (f')'(1).
ni 86. If f(x) = x+3 sin x + 2 cos x, find ( f')'(2).
ction:
87. Suppose that f and g are differentiable functions and let
bineg h(x) = f(x)g(x). Use logarithmic differentiation to derive the
Toisg formula
h' = g•f9¬l• fl + ( Inf) · fª•g'
bo bnil )2m/s
88. Use the formula in Exercise 87 to find the derivative.
(a) h(x) = x³
(b) h(x) = 3*
(c) h(x) = (sin x)*
-3
||
W piitive
increasing (and a are
both
the
creasing (e and
che Natural and Social Sciences ation
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