1. Let f(r) cosh(r) and a = 2. Let h 0.01 and approximate f'(a) using forward, backward and central differences. Work to 8 decimal places and compare your answers with the exact result, which is sinh(2).

Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - -x(²+y²). sec̟. tan?…

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Q: -sinh(x) at x = 0 is dx21 Answer:

A: Derivative of the function

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

Q: Evaluate dx dy in y=cosh(in e") b. 3x sinh (In x') 3x² sinh(In e* ) d. 3x sinh (3x² ) с. a. 3x…

A: Given:     y = cosh ( ln ex^3 )

Q: Differentiate  G(t)= Sinh(In t) G'(t)=?

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Q: 1. Find the derivative of the following using implicit differentiation. TYON b. BARZ c. y = sec(x +…

A: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question and…

Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

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Q: Differentiate the following functions in derivative and differential forms: f,(x) = Ax f,(x) = In x…

A: For f1(x)=Ax ⇒f'1(x)=Adxdx⇒f'1(x)=A Sketch of f1(x)=Ax limx→∞A=A

Q: Use differentials (or equivalently, a linear approximation) to approximate sin(40°) as follows: Let…

A: Given, f(x)=y= sin 40° Therefore, f'(x)= y'= dy/dx= d(sin 40°)/dx f'(x)= cos 40°

Q: 1) Find dy/dr by implicit differentiation. tan n'(xy"+y)= x

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Q: L(cos(at)sinh(at))

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Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: dy - år if y = In (sinh 50) and x = cosh 40 dx

A: Solving the problem by doing the derivative.

Q: Differentiate the following functions: S(x)= sinh* (v7x +1 tanh " (x* +2) +1) tanh" (x* +2) 3 a) b)…

A: Note    We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Show that the function below is contimuous but not differential atr= 0. r sin() if f(r) = 0. if r =…

A: Calculate RHL and LHL

Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: A particle moves along the x-axis with velocity given by v(t) = 67 sin (at) for time t> 0. If the…

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Q: Hiw proo p. s (sinh at) =_a s- at Notes at

A: Explained below

Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

A: Since you have posted multiple questions, we have solved the first question for you, if any specific…

Q: vatives for the following

A: Here we have;  y=lnlnsin-1(e2x)-5-lnx

Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x>0

Q: Can you help me with this problem step by step?

A: Given that

Q: d mula sinh (t) = In (t + VE? + 1) and- (In(t)) = } %3D ne derivative of sinh(t).

A: Here we use rule of differenciation to find the required derivative.

Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

Q: Find the surface area of revolution of 7 cos(5θ ) between - π/10 and  π/10, about the x-axis using…

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Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

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Q: Q2) A: Compute at the point (1, 0) for the function dx S(x,y) = cot 1(4x + em(sin2xy)) + sinh(3) +…

A: Given that, f(x,y)=cot-14x+elnsin 2xy+sin h(3)+log2x2 Which can be re - written as,…

Q: Find the si0pe of the given Function 1.) hlx) = sin x cos 3x at * = 3 メ 2.) y= In at メ = -2 メー! 3.)…

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Q: I Find the second derivative(y") of the following functions and simplify the final results. 4. y =…

A: 4 y = xcosx now fist derivative y' = x(cosx-1)cosx(-sinx) y' = (-1/2)sin2x x(cosx-1) now again…

Q: 6. y = In (e* + e") 7. y = tan e + etanax 8. y = In(x + Vř +1) 9 y = Arctan(;

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Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

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Q: 9. What is the derivative of cos(at5 + b) with respect to t?

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Q: 1. Find the derivative of the following functions (dy/dx) at x=Tt/4 cos x2 1– sin x2 y= 2. Find the…

A: We have to find the derivatives of given function at x=π/4  1. y= cosx2/(1-sinx2) 2. y=x3sin3xcos3x

Q: Suppose that the tangent line to the graph of f(x) = x(6*) at r = 1 is equal to the tangent line to…

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Q: ) Given the function f(x) derivative f"(1) with h, h/2 and h/4. 5. e Vx cos (Tx), approximate the…

A: Given function is  For this answer, we choose  We have  (up to 4 decimal place accuracy) We also…

Q: (g) y = Vtanh 3r (h) y= sinh(cosh 2.x)

A:

Q: 3. Calculate for one real root of tan x = 4x with xo = 1.2 up to four decimal places using the…

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Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: 1. Find for differentiate each of the following functions. dy хр a) (In(coshx) sinh x) g) y = - b) y…

A: Given: a)lncoshx3c)y+4coshx2=exsin-1(2x)g)y=sinhxex

Q: ydx -( x+***ty? dy = 0

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Q: 4. Evaluate if they exist: (a) sinh x dx (b) lim , sinh x dx r+00

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Q: Q:: If In/x2 + y² =sec(), use implicit differential to proof the following: - -x-(r+y?). sec. tan…

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Q: 1. Given dx [arccot u] = find the first derivative with respect to x of arccot v2x + 2. 1+u?

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Q: Find the derivative of the function. y = 6 In sin 22x O A. 24 sin 2x OB. 12 In sin 2x C. 24 cot 2x O…

A: We can find the derivative on the given function by using the chain  rule of differentiation.

Q: 2. Find the linear approximation to y = sinh (3x) at x=2. State your answer in both exact form and…

A: Find the linear approximation of f(x) at a point x=2

Q: H.W Ex.(8) Show that the functions f(x) = sin' () and ga)=2 tanv メ+) have the Same derivative.

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Q: 3. Evaluate the following derivatives: a) y = In[sinh(2x)] b) f(t) = tanh-1 VE

A: Derivative of the inverse hyperbolic function formula: -  ddx(sinhx)=coshx ddxtanh1x=12ln1+x1-x…