SECTION 3.4 EXERCISES Getting Started 1. How do you find the derivative of the product of two funetions that are differentiable at a point? How do you find the derivative of the quotient of two functions that are differentiable at a point? 2. 3. Use the Product Rule to evaluate and simplify ((x + 1)(3x + 2)). dx 4. Use the Product Rule to find f'(1) given that f(x) = x'e . Use the Quotient Rule to evaluate and simplify dx\3x + 2, 6. Use the Quotient Rule to find g'(1) given that g(x) r + 1 7-14. Find the derivative the following ways: a. Using the Product Rule (Exercises 7-10) or the Quotient Rule (Exercises 11-14). Simplify your result. b. By exparading the product first (Exercises 7-10) or by simplifving the quotient first (Exercises I1-4), Verify that your answer agrees with part (a). 7. f(x) = x(x - 1) 8. g(t) = (t + 1)(r - t + 1) 9. f(x) (x - )(3x + 4) 10. h(2) = (z' + 42 + z)(z = 11. f(w) = 4.s 12. g(s) 4s - 8s + 4s 4s 13. y where a is a constant 2ax + a 14. y where a is a constant 5.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (t –…

A: Here given function Now the fundamental theorem of calculus says

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(s) =…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 0. 0. X.…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. x. 4 g(x)…

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Q: Exercise 0.2.10: Find a solution to (x')² + x² = 4 using your knowledge of derivatives of function=…

A: As you ask multiple questions ,I only solve first one

Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

A: Part 1 of the Fundamental Theorem of Calculus says: Where, a=constant

Q: Find the derivatives of the functions in Exercise

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h(x)= […

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 4x F(x) = | cos (t) dt.…

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Q: Find the derivative of f(x) = (1 + 2x?)(x – x²) in two ways: by using the Product Rule and by…

A: According to product rule of differentiation, for two functions u(x) and v(x) ;…

Q: 3. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (1)…

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Q: 2. Find the derivative and the analytic domain of f(2) = 1+ %3D 22+1

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Q: Part 1 a) Given f (z) = + x2 + i(2x2 - y?), show which points where f has y a derivative. b) Show…

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Q: 2.Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function: g(x) =…

A: Given data: The expression for the give function is gx=∫0x1t3+1dt. The derivative of the given…

Q: Using the definition, find the derivative of f(z) = 3 z4-6 z? at point z= 0

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: Write true if the statement is correct and false if the statement is incorrect. Write your answer on…

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Q: EXAMPLE 2 Find the derivative of the function below. g(x) = 3 + t2 dt SOLUTION Since f(t) 3 + t2 is…

A: To find the derivative of the function

Q: Ise Part 1 of the Fundamental Theorem of Calculus to find the derivative of the fum 8(x) = [" 1 dt t…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(s) :…

A: Use fundamental theorem of calculus

Q: Jse Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h (x) = V5…

A: We area asked to find the derivative of the function using fundamental theorem of Calculus

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. F(x) 0. 5…

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

A: Fundamental Theorem of Calculus: If f(x) is continuous over an interval [a,b] and the function h(x)…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rcos(r) (3…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. = (s)6…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) =…

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Q: Find the derivative of g(x) using first principles. Show your steps. f (x) = %3D 1+3

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Q: 5. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. •cos…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = | : 1 -dt 1 + t5…

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y = (3 +…

A: Fundamental theorem of calculus Part -I :    If f(x) is continuous over an interval  a,b , and the…

Q: Find the derivative of h(x) = cos (2x3 - 5). %3D Provide your answer below: W(x)= O %3D

A: We will find the derivative of h(x) in the following step.

Q: Find the first derivative formula for the function g, by using the definition found in section 2.2.…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) =…

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Q: - Find the derivative of each Funeton of this by definition. 3 atx= 3 2 ソ=Vメナ1 ② ソーシィナ at メーネ V2X-3…

A: Since you have posted multiple questions so we solve the first three for you, to get the remaining…

Q: EXERCISES 2: Find the derivative of the function at Po in the direction of A. 1. f(x, y) = 2xy –…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 4 3 +2…

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Q: = [₁²₁ Use the Fundamental Theorem of Calculus, Part 1 to find the derivative of g (r) : = x² + 4dx.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. F(x) =  0…

A: By using part 1 of the fundamental theorem of calculus find the derivative of the function…

Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

A: Here given function

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) =…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of te function.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = 3t…

A: By fundamental theorem of calculus, we have

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan x V…

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