1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

Q: y = In (x* + 5)³

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Q: Compute the derivative of the function y = 5 sin-'(x) at the point x = (Use symbolic notation and…

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Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

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Q: 17) Find the first derivative of f(x) = (cos4x)6 6 or f(x) = cos 4x

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Q: ) y = In³ )) (tanh²(scc '(x²)

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Q: Find the derivative of the function. 1 - e3x = cos y = cos 1 + e3x y' =

A: Differentiate

Q: Solve for the derivative of the Hyperbolic Differentiation. 1. y = ex cos h 2x 2. y = ln sin h x…

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Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: | If In(x² – 3y) = x – y + 3 and y(-2) = 1, find y (-2) by implicit differentiation. y(-2) = An…

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Q: Find the derivative of y=cos4 x sin4 x Ans: 1/2 sin3 (2x) cos cos (2x) solution?

A: We simplify the given expression using the double angle property

Q: 2.) Find 1st derivative of y = e-'In (x-1)

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Q: Find the indicated nth derivative of the following: 1 7. 2nd derivative of y = xArcsinx + v1 – x²…

A: Find derivative using product rule and composition of functions rule

Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

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Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cose

A: The given function is : s(θ)=200sinθcosθ We need to find the derivative in two ways.

Q: 10. f(x) = cos (2x)e*²-1

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Q: y = x* + 2 sin(x) + xº + 24*.

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Q: 18) Find the first derivative of y = 1 -sin² x - 4

A: The given function is: y=14sin2x

Q: , find the derivative of y with respect to the appropriate variable 21. y = ln cosh y - 1/2 tanh2 y…

A: (21) Consider the provided equation, y=lncoshy-12tanh2y Find the derivative of y with respect to the…

Q: 5 Calculate the second and the third derivative of y = 6x – y": y"

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Q: 4. Find the derivative of g(x) = e5" sin(-x). Do not simplify.

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Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: Calculate up to 2nd derivative the equation g(x) = -8sin (*+1) %3D

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Q: Find the first derivative of: y = sinh e2" O y e2 cosh e2# 2e2" cosh e2" O y' 2 cosh e2 O y = cosh…

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Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

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Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

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Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

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Q: 4. Find the first derivative of y = 170x tan (20x)+- In(49 – x 5e7-8cos

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Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x…

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Q: Find the derivative of y = csc¯(In sin (x))

A: use simple integration formula.

Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

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Q: Find the derivative of y with respect to s. y= sec -1(9s5 + 5)

A: To find the derivative of  y=sec-1(9s⁵+5)

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

Q: Determine the first derivative of the ff. function a. y = 400(2)*+3 sin 3x b. y = Vxe2x cosx…

A: Given1) y=400(2)x+3sin3x2) y=xe2xcosx3)y=1+ln(3x2)1+ln(4x)We need to find the first derivative of…

Q: Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y…

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Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: Compute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)

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Q: Find the fourth derivative of the given: (Show complete solution from first to  fourth derivative)…

A: The function is given by y = (2x+1)25

Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = using a value…

A: Given function is y=sinx. We have to evaluate the first derivative of y=sinx at x=π2 using a value…

Q: Compute the derivative of h(sin(x)) at x = * assuming that h' (u)lu=0,5 = 10. (Use symbolic notation…

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Q: Obtain the derivative of the function y (ctg(5x))} y =- - sen? (5x) + 1

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Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

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Q: 1.Find the derivative of y = - arcsin %3D V4-x2

A: Given:        y=x4-x2-arcsinx2 differentiating on both sides     dydx=ddxx4-x2-arcsinx2…

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

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