Question 1: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 17 |" sin(t*) dt y = - tan x

Q: Question 3 Assume y is a differentiable function of x which satisfies the following equation: y2 +…

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Q: Question 8. By first writing 1 f(x) = in the form x² + 2)° (x2 + 2)°, where a < 0, obtain the…

A: f(x)=1x2+29 Lets first write it in the form (x2+2)a where a&lt;0 .

Q: Question 8 of 25 > Find the derivative of the function f. 3 √x f(x) = O At

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Q: Question 3 > Use part I of the Fundamental Theorem of Calculus to find the derivative of 14 dt f'(x)…

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Q: Find the first and second derivatives of the function  G(t) = 2 cos t - 3 sin t

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Q: Question 1 Find the derivative and simplify y cotVt-1 Oy-- Oy= - 2tt-1 1 2t/t-1

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Q: 1. Find the derivative of the following trigonometric functions a) y = x sin(x) + cos(x) b) y =…

A: Given the trigonometric function

Q: Question 9 Find the derivative of (3x+4)3 (-3x 2)4 h(x) = You should leave your answer in factored…

A: Given function isThe given function is a rational expression and the derivative can be obtained…

Q: 5. Find the derivative of each problem below, do not simplify. tan(2.x) f (x) = x² +2 а. b. f(x) =…

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Q: 25-32 Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Given an equation,

Q: Question 7 Let f(x) : (cot(x))ª. Use logarithmic differentiation to find an equation of the tangent…

A: Differentiate at given point then use equation of tangent line

Q: Question 20 Given the function fx) x to the 3" power 6x 2. find the walue of the first of the first…

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Q: Question 6 Find the derivative of the function y = 8ln(cos 2x)+ 5tan? (3x) Write the value of y' (0)…

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Q: QUESTION 2 Using Mean Value Theorem, Prove that if two differentiable functions f, g agree on…

A: Prove that if two differentiable functions f, g agree on their first derivatives, that is, f'=g'…

Q: Question 9 Suppose 8 (x) = sec-(x2). what is the derivative of g with respect to x? 2 A 8 (x) = x4-1…

A: We have to choose the correct answer from the given options according to the given information

Q: QUESTION 11 Find the derivative of the function at the given point in the direction of A. f(x, y) =…

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Q: Question 8 Let a be a real valued constant. Find the derivative with respect to x for the function…

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Q: Question 14 Use part I of the Fundamental Theorem of Calculus to find each derivative, given the…

A: Given query is to find the derivative of the expression.

Q: Question 2 of 6 Attempt 4 Find the equation of the tangent line to the function f(x) = 4* at x = 2.…

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Q: Question 5 b)

A: Please see the below picture for detailed solution.

Q: > Question 3 of 16 Determine the derivative of the function h with a domain {x | 0 x < T} cot (x)…

A: To find the derivative of the function h(x)

Q: Question 1 No decimal numbers allowed! a) Calculate the derivative of: In(r) f(x) = 3in(=) .…

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Q: Question 4 Given f(x) = x² – x 1) Derive the derivative function f'(x) using the limit definition of…

A: Solution is given below

Q: Question 2 Let a be a real valued constant. Find the derivative with respect to x: Y = 4ae 1-4ae4z O…

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Q: Part 1 Find the equation of the tangent line to the curve a(x) = 3 sin x+In(x2 - 5x +1) – e-6z at a…

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Q: Question 8 Use implicit differentiation to find the specified derivative at the given point. Find at…

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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 19 1. Find the function whose derivative is e¯(e* + 1)?

A: Let's find.

Q: Question 2 Find the derivative of f(x) = x³ cos(x)

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Q: Question 7 Apply the first principle of differentiation to find the derivative of ( a) f(x) = Vi-2x…

A: We use here first principle of Derivatives to obtain Differentiation.

Q: Problem 3. Consider the function Sa³ sin(1/x), x > 0. S(x) = 0, x < 0. (i) f'(0–). Compute the right…

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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 13 Find the second derivative of f(x) = x 3Inx O x(5+Inx) O 5x + Inx2 O x(5+Inx2) O 2x…

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Q: Question 12. Obtain the derivative of the function f(x) = sin(6x – 8) Enter the answer as a function…

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Q: Problem 4. Find a derivative A) Vy = xy+ cos y and %3D

A: The given function is y=xy+cosy

Q: Question No 02: Compute the first-order Derivative for each of the following functions at the…

A: Since you have multiple subparts, we will solve the first three subparts for you. To get remaining…

Q: Problem 9 Find the derivative of the function y = x? cos (3x2 – 1) Show all steps of your…

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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 10 Calculate the second derivative of the function y= In(cosx). -csc2x -sec?x c) cscx D)…

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Q: 7-46 Find the derivative of the function. 14. f(t) = t sin #t

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Q: Question 16 O [CLO-2] Find the derivative of f(x)=tan -¹ (√2x) O √√2x+√√88² (1+√√2x)² 1 √√√2x+√√2x³

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Q: Question 4. of S-dx as reverse or inverse differentiation, Given two nice functions f and g. Using…

A: Here we prove the linearity of the integration using the fact that integration is reverse…

Q: Question 26 Calculate the second derivative of the function y = In(cosx). A -sec'x B) -csc2x csc?x…

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Q: Question The derivative of the function y = cos(xln 3) log3(sin x) is:

A: We will find the derivative.

Q: 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find 14. h(x) = |" V1 + r³ dr the…

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Q: Question 1 a) Using the method of first principle find the derivative of the function 1 f (x) =

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Q: Question 3: a. Find the derivative of the function 2x +1(x - dx b. Given that y = 4x' -*, find dy…

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Q: Consider the function f (x) = x² -4 sin (x) 1. To use Newton Method, what will be the derivative of…

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Q: Question 12 VI² – 1 What is the derivative of y O y = 1 1 - 1 O y' %3| 22-1 O y' =

A: Given query is to find the derivative of the expression.

Q: Question 13 Let f (x) =x - sin(x²). what is the correct result of the derivative of f with respect…

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Q: QUESTION 3 Find the derivative for each of the following functions x? (а): x(х - 1) x² – 2x+1 - (b)…

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Q: > Question 4 of 16 Compute the derivative of h(t) t cot(t) 11 csc(t) (Use symbolic notation and…

A: Before we proceed, let's note that the derivative of:csc(x) = -csc(x)cot(x)cot(x) = -csc2(x)

Q: Question 12 Find the 2nd derivative (y") of y=√x ln x In 2

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Q: Question 4 Differentiate each of the following with respect to x using implicit differentiation. xy²…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: QUESTION 17 Solve the problem. Find the derivative of the function f(x y, z) = at the point (4.-4,…

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