Use the formulas given below to express tanh-1( - ) 6 logarithms. sinh - lu= In (ut Vư +1), uis any real number tanh 1 1 + u tanh 2 In ₁-₁ u<1 1-u csch-¹ u = In 1 u ¹ (-1)=( 6 + √1+u² |u| 2 cosh -¹ u = ln (u + √√²-1), uz 1 sech ¹u = In in terms of natural , u 0 coth¹u=- 1+√√1-u² u 1 u + 1 In 2 u-1' 2 |u|>1 0

Q: 3x+sinx-3 tan x -) Given g(x) = ln- calculate g'(x). %3D 3x4-Vx

A: Given gx=lnx3+sinx-3tanx3x4-x We know that lnab=lna-lnb. Therefore, using this formula we can write…

Q: I sin 2x cos 2x + kog log a|+e] Ans. y de Jogx

A: Given,

Q: csch-1 x= x = sinh sinh11 X Prove mathematically that the right-hand side is equal to the left-hand…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Differentiate. f(x) = x cos(x) sin(x) (please write it out on paper)

A:

Q: dx sech x (3 +5 sinh x)

A: Please see the explanation below.

Q: Salve for x if Arc tan (1- x) + Arc tan (1 + x) = Arc tan

A: Our Aim is to solve for 'x' if tan-11-x+tan-11+x=tan-1x -(i)

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

A: To prove the identity

Q: dr 1- y = Inlog 2- y = (cos x)*Snx 3- у e (sinx

A:

Q: The value of i log (x -i) + i? n + i³ log (x + i) + i* (2 tan-'x) where x > 0 and i = Fis

A: Introduction :

Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: f dx 3sinhx - 5 cosh x

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

A:

Q: sinh- x = In 2.

A:

Q: cosh(In x) dx

A:

Q: Simh3X= 3 Sinht+4 Sinh?x

A: This identity can be proved by using the properties and identities of hyperbolic functions. The…