Find Maclaurin expression of f(x) = Cosh (x)

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: Use mathematical induction to prove that the derivative of f (x) = xn equals nxn−1 whenever n is a…

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Q: Determine the absolute extreme values of the function f(x) = sinx - cosx + 6 on the interval 0 ≤ x ≤…

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Q: find f'(x) if f(x) = tanh(ln x) +sin2(2x)

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Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A: To find the antiderivative we integrate the given function c=integration constant

Q: Differentiate: (etan(x)) /(1+x)  Show all working out.

A: Given  etanx1+x. We have to differentiate it. Used formula:- ddxfxgx=gx⋅ddxfx−fx⋅ddxgxgx2 Here,…

Q: ln(x) is just defined for x greater than 1. Select one: True False

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Q: 1. Find the derivative of f(x) = tan³(sinx) + %3D

A: The given function isf(x)=tan3(sinx)+x3+3x4

Q: Find the derivative f'(x): f(x)=x4-x2+sin-1x/3 **4-x2 is under a radical sign!

A: Consider the given function f (x) taking (4-x^2) under the radical sign. Differentiate f (x) w.r.t x…

Q: 1 Using implicit differentiation, prove cot"x -- Make sure to show all work. dx 2 x* +1

A: Let  y=cot-1x Therefore: cot y=x

Q: Find the second derivative of the function 2 f(x) = sin (3x). Show your work.

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Q: If f(x) = x cosh æ + 3 sinh x then f'(x) =

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Q: 75. F(x) has a negative derivative over (-, 2) and (5,9) and a positive derivative over (2, 5) and…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Compute the derivative. k(θ) = θ2 sin2 θ

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Show that (x ln(x)) ‘ = 1 + ln(x) using the Product Rule for Differentiation.

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Q: compute the derivative.  f (x) = (cos2 x)cos x

A: To compute the derivative.  f (x) = (cos2 x)cos x

Q: Compute the derivative. f(x) = 7x sin (x) (Express numbers in exact form. Use symbolic notation and…

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Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

Q: Find the derivative. g(x) = cosh(In(x)) g'(x) = ||

A: To determine the derivative of the function.

Q: 3) Determine the derivative of f (x) = (2x)53*. 4) Determine the derivative of f (x) = sin…

A: 1. By using u.v rule 2. By using chain rule

Q: 2. Identify the derivative (9) based on the product rule ie, (G). Simplify to a single term.

A: Given ∂∂TGT

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: 1 Differentiate f(æ) = sin-(4x). Use exact values. = (x),f

A: We use the chain rule for differentiation

Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: compute the derivative g(x) = tan−1(ln x)

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Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: Find the second derivative of f(x) = 9 sin (2x). Enclose arguments of functions in parentheses. For…

A: On solving this we will get

Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

Q: (A) Prove that: cosh x + sinh x = e*

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Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: we have to find the second derivative of the function at the given point. f(x) = cos x2 , (0, 1)

Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…

A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…

Q: Find the 73rd derivative of the function f(x) = 2 sin(x). f (73) (x)

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Q: Prove the identity arcsinhx=ln(x+√1+x2).

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Q: Find the derivative y = (2 – x²) cos x + 2x · sinx 2 sin x – sin x (2 – x²) 2 cos x – sin x (2 – x²)…

A: Differentiate wrt x

Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…

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Q: How do you prove the general power rule of derivatives using the inverse property (x^n=e^(nlnx))?

A: The general power rule:

Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

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Q: Using method of sub., find the Anti-derivative 1 x In x

A: detailed solution is given below

Q: Find the derivative of f(x) = et tan( – 82° + 5a“). - f'(x) =

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Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: Find the equation of the tangent line to f(x) 16e* cos2(x) at x 4 (Use symbolic notation and…

A: To determine the equation of the tangent line.

Q: Differentiate the function. f(x) = sin(2 ln x)

A: Chain rule is use to find the derivative of composite functions

Q: 6: By use of the product rule, differentiate the function f (x) = (x² + 1) sin(2x).

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Q: Example38. From definition, find the derivative of cosx with respect to x.

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Q: Hi, I need help with this step-by-step please.

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Q: 27. Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Derivative of the function f(x) is given by

Q: compute the derivative. 19. y=(2cosθ+5sinθ)9

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Q: f(x) = In(sin² x)

A: Given,           fx=lnsin2x

Q: Compute f sin(cos(x²)) sin(x²)x dx

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