Question 2: dy a) Find for the following exponential function y = dx - 3e2x+1 -eV b) Using definition find the derivatives of In x

Q: e cos e d (Inly)) = ? %3D do Simplity dy= ? de Simplity

A: Explanation of the answer is as follows

Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: Question 2 If f(x) = S dt for x > 1, find f'(2). 1+lnt

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Q: 1. Find the derivative of each of the following: (a) y=e2* ln´(cos x) Do not simplify your answer.

A: We have to find the derivative of the function…

Q: y = log (cos(2x) );y'=* %3D %3D O 2 tan ( 2x ) / In (10) O - 2 tan ( 2x ) / In (10) O 2 cot ( 2x ) /…

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Q: (Question 12) Find the derivative dy for the function dx function y = arctan(3x – 4). Your answer…

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Q: Question 1. Identify the correct description for the formula (()a- (z)a), 4 (1)A from the following…

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Q: Question 8 Use differentials to find the approximate value of y: (2x 1)* when x = 0.98. O 0.88 O…

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Q: QUESTION 2 16х + 7 Solving the integral /. dx yields: бх2+х— 12 )3 In(2x+3) + –In(3x – 4) +c a.…

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Q: Question 1 Solve the following initial value problem: y" – Ay = 0 y'(0) = 1, y(0) = 0. Note that y"…

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Q: Use for question 1 1. Construct a slope field for the differential equation 2 = x + 2y dx

A: Slope is always dy/dx

Q: Question 2 > The function ` f(x) = (5 x-9)e^(-6 x) ` has one critical number. Algebrically use the…

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Q: QUESTION 4 Suppose that x2 -v3 +2xy= 12. Use implicit differentiation as presented in Section 14.5…

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Q: e2= (x² + 1)² 2/rª – 1 3. Find the derivative of y = ln Make any obvious simplifications. -

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Q: Question 6 Use differentials to find the approximate value of y: (2x 1) when x = 0.98. O (E) None of…

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Q: Question 4 a. Solve the following definite integrals. xp (* + x^€) ,'J (V&+1)* dx

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Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

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Q: 21. Which of the following is the third derivative of x? +y? = a?? A. ya - Sar С. y -3ax В. -7ar D.

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Q: Question 4: Confirm that the function you found is a solution to the differential equation z' + z =…

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Q: ソ= 9+8 e cos e dLinly))= ? Simplified dy = ? %3D de Simprified

A: Explanation of the answer is as follows

Q: Question 7 Solve for the differential ofy when y=sinx, x=-, and dx=- 3 2 A 4 B 元 4.

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Q: Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

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Q: What is the relationship between the functions In r and e?

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Q: CL Activity # 4 # 19 III. Find the derivative of the following using implicit differentiation. 19. e…

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Q: Question 9 Let y = tan e find the differential dy of the function. O dy = e (r – 1) sec e- da O dy =…

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Q: Example: Find dy de (a) ey sin x = x + xy (b) y = x² sin¬'(3x² – 1) (c) y = x* (Hint: Use…

A: Using product rule of Derivative

Q: 3. Find the derivative of the given exponential function w e2t (2 cost + sin t)

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Q: What is the derivative of y log b ( cos? (ax) ? Note that a and b are real numbers. A - 2 a log ble)…

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Q: Question 11 d²y is Blank 1. Find the second derivative of y= (x+5)² The dx- Blank 1 Add your answer

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Q: y=24x dy/dx=_____? 2. Find the derivative of the following function. A=860(1.610)t A'=_____?…

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Q: 1. Find S*-3**+ dx by hand and show how to check the result is correct by differentiation.

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Q: Question 6 Consider the function below: sin(x²+y) { (x, y) # (0,0) (x, y) = (0,0) f(æ, y) y-x Find…

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Q: Question 8 Integrate the function. dx V9 - x2 COs:1 X+C 2 cos x+ sin x+C D sin *-C Question 9 413

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Q: Find exact value(s) for x such that 3e" - e' = 0.

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Q: Example: Find de dy (a) eª sin x = x + xy (b) y = x² sin-1 (3x² – 1) (c) y = x* (Hint: Use…

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Q: 2. In π 2 π ln - 4 e* cos(ex) dx

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Q: Question 001: Complete the following question involving Substitution Method. Given the integral 2x +…

A: Given:∫e2x+7dx

Q: Question 4: Confirm that the function you found is a solution to the differential equation z' + z =…

A: The differential equation is given as z'+z = cos(2t) Corresponding homogeneous equation is given as…

Q: Question 8 Find the derivative of the function at Po in the direction of f(x, y) = 3x 2 + 4y, P o(8,…

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Q: Question 5 Let y = 4x2. a) Find the change in y, Ay, when r = 2 and A x = 0.2 b) Find the…

A: Given equation         y=4x² We have to apply the partial differentiation for the equation

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) = -M1+ tanh 2 satisfies the…

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Q: Question 5 4x2 Calculate the integral: dx 5+ x² V5 + x² - 10 ln V5 2х + C (5 + x²) 32 V5 + x2 V5 2х…

A: Indefinite Integration

Q: Find the derivative of the logarithmic function. y = In 6 + e 6- e*. Step 1 The given function y =…

A: We will derivate the function step wise as asked in the question.

Q: Question 6 Differentiate: y = arccot (x) + arctan 2 + x 1 - 2x 0 1 (E) None of these O:2x O 1-2x

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Q: d. Show that sin ž is exists or not? e. Verify that the derivatives of sinh z. f. Solve the value of…

A: The solution are next step

Q: Question 7 1 Solve for the differential of y when y = sinxx, x=-, and dx =- 2 3 A B 4 -- 4 D 2

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Q: Question 6 Determine the derivative, y': y = log, (In a?) %3D Oy = z In 5 In a Oy = = z In 5 In z Oy…

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Q: (1–2x)3 1+x2 dy Question (4): Find by logarithmic differentiation for f (x) dx

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Q: Question 4 Use Laplace transforms to solve the differential equation: d²x d1² Cos (21) + 4x=cos!…

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Q: Activity 6: Find the first and the second derivative of the following: 1. у 3D е cos x 2. y = sin³…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…