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Math
Calculus
Calculus, Early Transcendentals
Chapter 3.2, Problem 34E
Chapter 3.2, Problem 34E
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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3.1 Derivatives Of Polynomials And Exponential Functions
3.2 The Product And Quotient Rules
3.3 Derivatives Of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives Of Logarithmic And Inverse Trigonometric Functions
3.7 Rates Of Change In The Natural And Social Sciences
3.8 Exponential Growth And Decay
3.9 Related Rates
3.10 Linear Approximations And Differentials
3.11 Hyperbolic Functions
Chapter Questions
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Problem 1E: Find the derivative of f(x) = (1 + 2x2)(x x2) in two ways: by using the Product Rule and by...
Problem 2E: Find the derivative o f the function F(x)=x45x3+xx2 in two ways: by using the Quotient Rule and by...
Problem 3E: Differentiate. 3. y=4x2+3(2x+5)
Problem 4E: Differentiate. 4. y=10x2+7x22x2
Problem 5E: Differentiate. 5. y=x3ex
Problem 6E: Differentiate. 6. y=ex+22ex1
Problem 7E: Differentiate. 7. f(x)=3x25xex
Problem 8E: Differentiate. 8. g(x)=(x+2x)ex
Problem 9E: Differentiate. 9. y=xex
Problem 10E
Problem 11E: Differentiate. 11. g(t)=32t5t+1
Problem 12E: Differentiate. 12. G(u)=6u45uu+1
Problem 13E: Differentiate. 13. f(t)=5tt3t1
Problem 14E
Problem 15E: Differentiate. 15. y=sss2
Problem 16E: Differentiate. 16. y=xx+1
Problem 17E: Differentiate. 17. J(u)=1u+1u2u+1u
Problem 18E
Problem 19E: Differentiate. 19. H(u)=(uu)(u+u)
Problem 20E
Problem 21E: Differentiate. 21. V(t)=t+2ett
Problem 22E
Problem 23E: Differentiate. 23. y=ep(p+pp)
Problem 24E
Problem 25E: Differentiate. f(t)=t3t3
Problem 26E: Differentiate. 26. y=z2+ezz
Problem 27E: Differentiate. f(x)=x2exx2+ex
Problem 28E
Problem 29E: Differentiate. f(x)=xx+cx
Problem 30E: Differentiate. f(x)=ax+bcx+d
Problem 31E
Problem 32E: Find f'(x) and f"(x). f(x)=xex
Problem 33E
Problem 34E
Problem 35E
Problem 36E: Find an equation of the tangent line to the given curve at the specified point. y=1+x1+ex,(0,12)
Problem 37E
Problem 38E
Problem 39E: (a) The curve y = 1/(1 + x2) is called a witch of Maria Agnesi. Find an equation of the tangent line...
Problem 40E: (a) The curve y = x/(1 + x2) is called a serpentine. Find an equation of the tangent line to this...
Problem 41E: (a) If f(x) = (x3 x)ex, find f'(x). (b) Check to see that your answer to part (a) is reasonable by...
Problem 42E: (a) If f(x) = (x2 1)/(x2 + 1), find f'(x) and f"(x). (b) Check to see that your answers to part (a)...
Problem 43E: If f(x) = x2/(l + x), find f"(1).
Problem 44E: If g(x) = x/ex. find g(n)(x).
Problem 45E: Suppose that f(5) = 1, f'(5) = 6, g(5) = 3, and g'(5) = 2. Find the following values. (a) (fg)'(5)...
Problem 46E: Suppose that f(4) = 2, g(4) = 5, f'(4) = 6. and g'(4) = 3. Find h'(4). (a) h(x) = 3f(x) + 8g(x) (b)...
Problem 47E: If f(x) = exg(x), where g(0) = 2 and g'(0) = 5, find f'(0).
Problem 48E: If h(2) = 4 and h'(2) = 3, find ddx(h(x)x)|x=2
Problem 49E: If g(x) = xf(x), where f(3) = 4 and f'(3) = 2, find an equation of the tangent line to the graph of...
Problem 50E: If f(2) = 10 and f'(x) = x2f(x) for all x, find f"(2).
Problem 51E: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). (a)...
Problem 52E: Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown....
Problem 53E: If g is a differentiable function, find an expression for the derivative of each of the following...
Problem 54E: If f is a differentiable function, find an expression for the derivative of each of the following...
Problem 55E: How many tangent lines to the curve y = x/(x + 1) pass through the point (1, 2)? At which points do...
Problem 56E: Find equations of the tangent lines to the curve y=x1x+1 that are parallel to the line x 2y = 2.
Problem 57E: Find R'(0), where R(x)=x3x3+5x51+3x3+6x6+9x9 Hint: Instead of finding R'(x) first, let f(x) be the...
Problem 58E
Problem 59E
Problem 60E: A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric...
Problem 61E: The Michaelis-Menten equation for the enzyme chymotrypsin is v=0.14[S]0.015+[S] where v is the rate...
Problem 62E
Problem 63E: Extended Product Rule The Product Rule can be extended to the product of three functions. (a) Use...
Problem 64E: (a) If F(x) = f(x) g(x), where f and g have derivatives of all orders, show that F" = f"g + 2f'g' +...
Problem 65E
Problem 66E
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