Question 24 The slope of the tangent line to f(x)= cos(x)· sin(x) at x = is ... ANSWER: Blank 1 Blank 1 Add your answer Question 25 Given f(x) = e"ln(x), f'(1) = ... ANSWER: Blank 1 Blank 1 Add your answer

Q: Question 6 4 pts For which x-value(s) is the tangent line to the curve y=tan x parallel to the line…

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Q: Question (3): Sketch the graph of the following function y = -2 tanx- 1 Question (4): Find the first…

A: Our objective is to draw the graph of  a function, and find the derivative of a function.

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

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Q: Question 17 Using the definition of a derivative, find s' (r) given s() =-x2 2x +3. Do not include s…

A: Given:

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

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Q: Question 9 What is the derivative of y log b ( cos? (ax)) ? Note that a and b are real numbers. A 2…

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Q: Find the equations of the tangent line and normal lines to the graph of the function f(x)= —4 sinx…

A: We have to find

Q: Question 5 Which of the following statements are true and which are false? I. Given an equation…

A: To write the true and false

Q: QUESTION 11 Find an equation of the tangent line to the curve at the point corresponding to the…

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Q: Question 5. Find the equations of the tangent line and the normal line (normal is perpen- dicular to…

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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 (4): Find the first derivative of the following function: y = sin (x – x2)

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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 2. Find the derivative of the given functions: a) y = e5 log, (4x® + e2=) In(x² + 4)ez b) y…

A: We know that u·v' = u·v' + v·u' uv' = v·u'-u·v'v2

Q: Find a > 0 such that the tangent line to the graph of f(x) = x?e=* at x = a passes through the…

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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: Find the equations of the tangent line and normal lines to the graph of the function f(x) = 3 sin x…

A: Given,  fx = 3sinx  We have to find the equation of tangent line and normal line at x = π2

Q: d Find the derivative e" + sin ax] dx e" – a cos (ax) e" + a sin (ax) e" + a cos (ax) e" + sin (ax)

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Q: Question |–2x – 4 3x3. V 3x3 using logarithmic differentiation. 6 Find the derivative of the…

A: Some properties of logarithm are: logxy=logx+logy logxy=logx-logy logxn=nlogx

Q: Question 3 3.1 Given that: x*y? + cosh(3y + x²) = 2y³ Use implicit differentiation to find . Show…

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Q: Question 1 (a) Find of the following functions by implicit differentiation (i) Vxy = 1+ x?y (ii) sin…

A: Since you have posted multiple questions i can do first question (a)with all parts as per our…

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 1 dy (a) Determine dx of the following function sinhx x+y = V1+cosh x po.s 5x+3 -dx. Give…

A: The given problem is to find the derivative of given function and evaluate the following integral…

Q: Question 5 Determine the derivative of the given function: y = (e + e)3 O y = 3(e- + e")² (e- + e")…

A: The derivative is given below.

Q: PART B QUESTION 1 I 1 dy Find the derivative Y for the function y = x° tan6x + dx QUESTION 2

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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 17 df Calculate the derivative (1) = dæ where f (x) xe". O 2e No answer text provided. O 1

A: We know, ddx(ex)=exddx(x)=1

Q: Find dy/dx, using implicit differentiation. HINT [See Example 1.] y In x + y = 9 Compare your answer…

A: We are required to find its implicit differentiation. After we have to differentiate if for y as a…

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 (4): Find the first derivative of the following function: y = sin (x - x*)

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Q: QUESTION 3 3 Given that f(x) x+1 a) Find f'(x) using the definition of derivative. b) Find the…

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Q: In a 24-hour period, a human's body temperature will vary ab When at rest (usually at night), the…

A: The derivative of a function of a real variable measures the sensitivity to change of the function…

Q: Question 4 Determine the derivative of the given function: y = (e + e*)3 Oy = 3(e+e) (e" - e) Oy =…

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Q: Question three [10] i. Find the value of the derivative of f(z)=z+2z -i at z=3+2i

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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 21 Find the equation of the tangent line to y = x = 1. at A y - Vi = - Vi (x – 1) B VE (x -…

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Q: QUESTION 18 Find the equation of the tangent line at y = 0, given the inverse function x = (3y +…

A: First find slope then use equation of tangent line

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: To find the equation of the tangent line to the graph of the equation ln(x) + xe^y = 1 at the point…

A: Given query is to find the tangent line.

Q: 51. The horizontal range R of a projectile launched from ground level at an angle e and initial…

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Q: QUESTION 11 Find the equation of the tangent line at y = 0, given the inverse function x = (3y +…

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Q: 5) Find the derivative of h(0) = tan 50. d 6) Find dy (cot y).

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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: Function 1 t h(t) = sin t+=e 5 Point πT 1 I, -e 5 (a) Find an equation of the tangent line to the…

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Q: Question 5 Consider the function f(x, y, z) = x cos(xy² z). Compute the value of the derivative fr…

A: Solution

Q: Question 3 (a) Find the first and second derivative of the following function, in which a and b are…

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Q: cos(x) 1– sin(x) 12. У | 22. Find an equation of the tangent line to the curve at a given point y =…

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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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