The value of (i)' is = ... O T/2 O T/2 O e^(-T/2) O e^(Tt/2)

Q: Explain the method of proving the derivative (dy/dx) of sinh(x) and cosh(x) ?

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Q: 3 dx|

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Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: Use differentials to estimate the value of 7+(1.02) correct to four decimal places.

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Q: dy Find by implicit differentiation dx хЗу — ху3 — а3Ьз

A: Given:- x3 y -xy3 =a3 b3  To find:- dydx of given implicit function

Q: find the derivative.

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Q: Use differentials to approximate the quantity   √17

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Q: 1) [(sinh 2x + cosh2x)° dx

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Q: Find the derivative of ¤(x) at x = /3/2 where rsin-'(x) $(x) = eº tan 0 do. x2

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Q: (A) Ln(2) S Sinh(x) Cosh² (x) dx

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Q: You would like to use differentials to approximate the change in BMI when weight increases from 55…

A: Given: The function represents body mass index(BMI) is  Bw,h=wh2 where, w means weight in kilograms…

Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…

Q: Find the equilibria of the differential eq

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Q: Evaluate S sinh x cosh x dx by letting u=cosh x

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

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Q: Find the derivatives of the functions in Exercis

A: Chain Rule: f(g(x))'=f'(g(x))g'(x) Differentiation formulae: ddxsinx=cosxddxcosx=-sinxddxax=a

Q: What is the derivative of ln(sin x + cos x)

A: Consider the given function:

Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: Find the derivative of ,In sin-1) y = e %3D

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Q: Find dy/dx by implicit differentiation. x4 + yA 5

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Q: Find the first derivative of: sin(x+y)+cos(x-y)=3

A: Given,           sinx+y+cosx+y=3 The objective is to find the first derivative.

Q: sin 0 r (0) = log„(ršin ® – sin" 0)

A: We know that, from the derivative formulas ddxax=axloga       ⋯⋯1ddxlogx=1x…

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: find integral sec 3 x dx

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Q: 7 dy if Use implicit differentiation to find 8. dx dy dx +

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Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

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Q: What is the derivative of y = e3 In(5 + e3)? %3D

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Q: 8. The value of f sinh* x cosh³ x dx

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Q: 3 sinº x dx 4 Show that

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Q: 3- - 플 플 sin²cyl y จน

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Q: What is the derivative of: y = ln ln(1 − cos x)

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Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

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Q: Find cosh æ In(sinh x)dx.

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Q: -1/7 17 dx =?

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Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

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

A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…

Q: N= cos(5x) (SX メコ

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Q: 7) Find the average rate of change of the function A(x) = sin ( 2x - -) from x = to x =

A: A(x) = sin(2x - π/6) A(x2) = A(5π/6)          = sin(2*5π/6  - π/6)          = sin (9π/6)          =…

Q: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: dy Find by implicit differentiation. dx ху — ху" %3 8 -

A: Implicit differentiation: Differentiate both sides of an equation with two variables by considering…

Q: Find the equation of the tangent line to the curve y = ln(4 ln x) at the point where x = e. %3D

A: It can be solved using differentiation.

Q: Find dy/dx by implicit differentiation. 3x +у - 2 + х?у? У 3

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Q: tanh 2x In (cosh 2x)dx

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Q: · Find dy/dx by implicit differentiation. 6. 2x? + ху — у? — 2

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Q: cosh(In x) dx

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Q: dx =?

A: we have to solve integration

Q: What is the derivative of: 4 ln(sec y + tan y) − 2x − sin 2x = 1

A: Given: 4 lnsec y+tan y-2x-sin 2x=1 To Find: dydx=?

Q: The derivative of: y =0(sin (In (0)))+cos(In (0 )) is:

A: Given :y=θ(sin(ln θ))+ cos ln θ dydθ=θcos ln θθ+sin ln θ-sin  lnθ θ      =cos ln θ+sin ln θ-sin  lnθ…

Q: Find the derivative of s(*) - L Int dt 1+t

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Q: -1/16 dx =

A: Integration