4. Determine the following derivatives without simplifying either before or after. (YOU MAY USE ANY TECHNIQUE COVERED IN THE COURSE TO EVALUATE THE DERIVATIVES.) (AT MOST 75% CREDIT IF YOU SIMPLIFY EITHER BEFORE OR AFTER.) -[sinh(x)(x² + 7*)] a. dx 10 d [In(x² – 4x + 13) + sin(xx) b. dx 10 d? sin dx2 с.
4. Determine the following derivatives without simplifying either before or after. (YOU MAY USE ANY TECHNIQUE COVERED IN THE COURSE TO EVALUATE THE DERIVATIVES.) (AT MOST 75% CREDIT IF YOU SIMPLIFY EITHER BEFORE OR AFTER.) -[sinh(x)(x² + 7*)] a. dx 10 d [In(x² – 4x + 13) + sin(xx) b. dx 10 d? sin dx2 с.
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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Question
Only solve d, and please only solve by using the formulas given. Thanks
(P4.2)
![4. Determine the following derivatives without simplifying either before or after.
(YOU MAY USE ANY TECHNIQUE COVERED IN THE COURSE TO EVALUATE THE DERIVATIVES.)
(AT MOST 75% CREDIT IF YOU SIMPLIFY EITHER BEFORE OR AFTER.)
-[sinh(x)(x² + 7*)]
a.
dx
10
d [In(x² – 4x + 13) + sin(xx)
b.
dx
10
d?
sin
dx2
с.
10
d.
tan(t )dt
xp
10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73b00b2a-4fa8-4b66-93aa-a27c1d9b51ff%2F5a0b634a-cb25-45f3-8e09-b8c8b8e97bd3%2F9dkbqp3j_processed.png&w=3840&q=75)
Transcribed Image Text:4. Determine the following derivatives without simplifying either before or after.
(YOU MAY USE ANY TECHNIQUE COVERED IN THE COURSE TO EVALUATE THE DERIVATIVES.)
(AT MOST 75% CREDIT IF YOU SIMPLIFY EITHER BEFORE OR AFTER.)
-[sinh(x)(x² + 7*)]
a.
dx
10
d [In(x² – 4x + 13) + sin(xx)
b.
dx
10
d?
sin
dx2
с.
10
d.
tan(t )dt
xp
10
![FUNDAMENTAL THEOREM OF CALCULUS I
If fis continuous on [a,b] then the function
BASIC ANTIDERIVATIVES
Constant
= ax +C, where a ER
%3D
Power:
is continuous on [a, b], dfferentiable on (a, b) and gʻ'(x) = f(x).
(rds =
+C, where r + - 1
r +1
FUNDAMENTAL THEOREM OF CALCULUS II
If fis continuous on [a,b] and F is any antiderivative of f, then
= In |x|+C
Exponential:
f(x)dx = F(b) – F(a).
b
+C, where b E (0,00)
In(b)
Trigonometric:
NET CHANGE THEOREM
cos(x)dx = sin(x) +C
If F' is continuous on [a, b), then
Jamer-
sec-(endx = tan(x) + C
= - cos(x) +C
F(x)dx = F(b) – F(a).
VARIABLE SUBSTITUTION
sec(x)tan(x)d x = sec(x) + C
If u = g(x) is differentiable whose range contains [a, b] and fis
continuous on [a, b), then
Joscondx = - cot(2) + C
r)cot(x)dx = - csc(x) +C
VARIABLE SUBSTITUTION FOR DEFINITE INTEGRALS
tan(x)dx = - In|cos(x)|+C_
If u = g(x) is differentiable whose range contains [a, b] and fis
continuous on [a, b), then
Jcot(o)d x = In |sin(<)| + c
f(u)du.
sec(x)dx = In|sec(x) + tan(x)| + C
gla)
x)dx = In[cse(x) – cot(x)| +C
VOLUMES OF SOLIDS OF REVOLUTION
Inverse Trigonometric:
Revolving about x Revolving about y-
xp
= arcsin(x) + C, where x *±1
-ахis
axis
Disks/Washers Integrate x variable Integrate y variable
dx
= arctan(x) + C
1+x2
Cylindrical Shells Integrate y variable Integrate x variable
Нурerbolic
AVERAGE VALUE OF A FUNCTION
cosh(x)d x = sinh(x) +C
Iffis continuous on [a, b], then
sinh(x) +C = cosh(x) + C
Savg =
f(x)dx.
b- a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73b00b2a-4fa8-4b66-93aa-a27c1d9b51ff%2F5a0b634a-cb25-45f3-8e09-b8c8b8e97bd3%2Fljm5ly_processed.png&w=3840&q=75)
Transcribed Image Text:FUNDAMENTAL THEOREM OF CALCULUS I
If fis continuous on [a,b] then the function
BASIC ANTIDERIVATIVES
Constant
= ax +C, where a ER
%3D
Power:
is continuous on [a, b], dfferentiable on (a, b) and gʻ'(x) = f(x).
(rds =
+C, where r + - 1
r +1
FUNDAMENTAL THEOREM OF CALCULUS II
If fis continuous on [a,b] and F is any antiderivative of f, then
= In |x|+C
Exponential:
f(x)dx = F(b) – F(a).
b
+C, where b E (0,00)
In(b)
Trigonometric:
NET CHANGE THEOREM
cos(x)dx = sin(x) +C
If F' is continuous on [a, b), then
Jamer-
sec-(endx = tan(x) + C
= - cos(x) +C
F(x)dx = F(b) – F(a).
VARIABLE SUBSTITUTION
sec(x)tan(x)d x = sec(x) + C
If u = g(x) is differentiable whose range contains [a, b] and fis
continuous on [a, b), then
Joscondx = - cot(2) + C
r)cot(x)dx = - csc(x) +C
VARIABLE SUBSTITUTION FOR DEFINITE INTEGRALS
tan(x)dx = - In|cos(x)|+C_
If u = g(x) is differentiable whose range contains [a, b] and fis
continuous on [a, b), then
Jcot(o)d x = In |sin(<)| + c
f(u)du.
sec(x)dx = In|sec(x) + tan(x)| + C
gla)
x)dx = In[cse(x) – cot(x)| +C
VOLUMES OF SOLIDS OF REVOLUTION
Inverse Trigonometric:
Revolving about x Revolving about y-
xp
= arcsin(x) + C, where x *±1
-ахis
axis
Disks/Washers Integrate x variable Integrate y variable
dx
= arctan(x) + C
1+x2
Cylindrical Shells Integrate y variable Integrate x variable
Нурerbolic
AVERAGE VALUE OF A FUNCTION
cosh(x)d x = sinh(x) +C
Iffis continuous on [a, b], then
sinh(x) +C = cosh(x) + C
Savg =
f(x)dx.
b- a
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