Q7,Q11&Q15As these are very easy questions so solve all three questions in the order to get positive feedbackPlease solve both questions correctly in 30 minutes and get the thumbs up please show neat and clean work for itBy hand solution needed 102 CHAPTER 1 The DerivativeCheck Your Understanding 1.61. Find the derivativedx (x).EXERCISES 1.6Differentiate.1. y = 6x³3. y=3√x5.ya_27. f(x)=x+x³+x9. y = (2x+4)³11. y=(x³ + x² +1)13. y=-=15. y=3√2x²+117. y = 2x + (x + 2)³19. y = 1= 5x5121. y ³+1123. y=x+x+125. f(x)=5√3x³ + x27. y= 3x + 7³29. y= V1+x+x²21-5x31. y T451 + x + √x35. y=x+1+√x+137. f(x) =33. y=-22. y =24. y = 2√x+11x³ + x + 1V1+x²12x+57VI+x34. y=(1+x+x²)26. y28. y=30, y =32. y=-2. y = 3x44. y=_1_3.x²6. f(x) = 12 + 7/38. y = 4x³ - 2x²+x+110. y=(x²-1)³12. y = (x² + x)-214. y - 4(x²-6)-316. y = 2√x+118. y (x-1)³ + (x+2)*20. y(x²+ 1)² + 3(x² - 1)²im36. y = ²x8. y = (x - 1) ¹y=39. f(x)=3x² - 2x + 1, (1, 2)40. f(x) = x10 + I + VI − x, (0, 2)1/(a+h)+ g(a+h)]-[f(a)+ g(a)h[f(a+h)-f(a) g(a+h)-g(a)hhf(a+h)-f(a)h-f(a)+g'(a).In Chapter 3, the general power rule will be proved as a special case of the chain rule.-limIn Exercises 39 and 40, find the slope of the graph of y=f(x) at thedesignated point.-limg(a+h)-g(a)h+limSolutions can be found following the section exercises.x + (x³ + 1) ¹02. Differentiate the function yLimit of a sum.41. Find the slope of the tangent line to the curve y = x³ + 3x - 8at (2,6).42. Write the equation of the tangent line to the curvey=x+3x-8 at (2,6).43. Find the slope of the tangent line to the curve y(x²-15)6at x4. Then write the equation of this tangent line.44. Find the equation of theangent line to the curvey" x²+x+2at x = 2.45. Differentiate the function f(x)-(3x²+x-2)² in twoways.(a) Use the general power rule.(b) Multiply 3x²+x-2 by itself and then differentiate theresulting polynomial.46. Using the sum rule and the constant-multiple rule, show thatfor any functions f(x) and g(x)8 muavesty6r+1f(x)-8(x)=f(x)-8(x)dx47. Figure 2 contains the curves y = f(x) and y= g(x) and thetangent line to y=f(x) at x = 1, with g(x)=3-f(x). Findg(1) and g'(1).y = f(x)dy = g(x)Figure 2 Graphs of f(x) and g(x) = f(x).x

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Q7,Q11&Q15As these are very easy questions so solve all three questions in the order to get positive feedbackPlease solve both questions correctly in 30 minutes and get the thumbs up please show neat and clean work for itBy hand solution needed 102 CHAPTER 1 The DerivativeCheck Your Understanding 1.61. Find the derivativedx (x).EXERCISES 1.6Differentiate.1. y = 6x³3. y=3√x5.ya_27. f(x)=x+x³+x9. y = (2x+4)³11. y=(x³ + x² +1)13. y=-=15. y=3√2x²+117. y = 2x + (x + 2)³19. y = 1= 5x5121. y ³+1123. y=x+x+125. f(x)=5√3x³ + x27. y= 3x + 7³29. y= V1+x+x²21-5x31. y T451 + x + √x35. y=x+1+√x+137. f(x) =33. y=-22. y =24. y = 2√x+11x³ + x + 1V1+x²12x+57VI+x34. y=(1+x+x²)26. y28. y=30, y =32. y=-2. y = 3x44. y=_1_3.x²6. f(x) = 12 + 7/38. y = 4x³ - 2x²+x+110. y=(x²-1)³12. y = (x² + x)-214. y - 4(x²-6)-316. y = 2√x+118. y (x-1)³ + (x+2)*20. y(x²+ 1)² + 3(x² - 1)²im36. y = ²x8. y = (x - 1) ¹y=39. f(x)=3x² - 2x + 1, (1, 2)40. f(x) = x10 + I + VI − x, (0, 2)1/(a+h)+ g(a+h)]-[f(a)+ g(a)h[f(a+h)-f(a) g(a+h)-g(a)hhf(a+h)-f(a)h-f(a)+g'(a).In Chapter 3, the general power rule will be proved as a special case of the chain rule.-limIn Exercises 39 and 40, find the slope of the graph of y=f(x) at thedesignated point.-limg(a+h)-g(a)h+limSolutions can be found following the section exercises.x + (x³ + 1) ¹02. Differentiate the function yLimit of a sum.41. Find the slope of the tangent line to the curve y = x³ + 3x - 8at (2,6).42. Write the equation of the tangent line to the curvey=x+3x-8 at (2,6).43. Find the slope of the tangent line to the curve y(x²-15)6at x4. Then write the equation of this tangent line.44. Find the equation of theangent line to the curvey&#34; x²+x+2at x = 2.45. Differentiate the function f(x)-(3x²+x-2)² in twoways.(a) Use the general power rule.(b) Multiply 3x²+x-2 by itself and then differentiate theresulting polynomial.46. Using the sum rule and the constant-multiple rule, show thatfor any functions f(x) and g(x)8 muavesty6r+1f(x)-8(x)=f(x)-8(x)dx47. Figure 2 contains the curves y = f(x) and y= g(x) and thetangent line to y=f(x) at x = 1, with g(x)=3-f(x). Findg(1) and g'(1).y = f(x)dy = g(x)Figure 2 Graphs of f(x) and g(x) = f(x).x

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