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 expand_more
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 expand_more
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 format_list_bulleted
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