In Exercises 25–36, find the derivative of y with respect to the appro- priate variable. 25. y = sinh Vĩ 26. y = cosh¯|2Vx + 1 28. y = (0² + 20) tanh¯' (0 + 1) 27. y = (1 – 0) tanh¯! 0 29. y = (1 – t)coth¬l Vt 31. y = cos!x – xsech¯'x 30. y = (1 – f)coth¯'t 32. y = In x + V1 – x²sech¯!x 33. y = csch¯ 34. y = csch| 2º 35. y = sinh'(tan x) 36. y = cosh¯1 (sec x), 0 < x < #/2 Integration Formulas

Q: findthe differential dy of the given function. y= arctan(x − 2)

A: we have to find the differential dy of the given function. y= arctan(x − 2)

Q: 1 The derivative of the function y = cos V at z e = is equal to 4.

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Q: 9. The anti-derivative of the function f(x) = e² + cost is (a) e²+ sinx+c (b) e² - tanz+c 10. 0.5(x…

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Q: In Exercises priate variable. 21. y = cos (r) 23. y = sin-'V21 25. y = sec (2s + 1) find the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: Find the differential dy of the given function y=extanx

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Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

Q: Explain of the method of proving the derivative (dy/dx) of y=U(x)ᵛ⁽ˣ⁾ where U(x) and V(x) are…

A: y=uxvx, where ux  &amp;  vx are the differential functions of x. To differentiate these type of…

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

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Q: Find the differential dy of the given function. y sec² x x² + 2 dy sec²x(x²+2)tan x-x (x² + 2)² dx X

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Q: Find the differential d8y of the function y=exsinx.

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Q: y +y= secx

A: We have to solve the problem

Q: 9. Find dy/dx by implicit differentiation of y? = In(x), at (e36,6).

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Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: Verify that the indicated family of functions is a solution of the given differential equation.…

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Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y =…

A: Given y=lnex+e-x To find y'':

Q: The function y(x) is defined by the implicit equation x2−√ylny=1. Find its differential at the point…

A: Differentiate both sides with respect to x and solve for dy/dx

Q: (5) Find the derivative dy/dx, where: 4 1 -1 y=- y = cosec(cot3x), y=Vsinh¯3x 3 1+ cos° x

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y =…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: 5. а) Find the derivative of y = (cosh r)*. Show that the function y = e -2" (sin 3x + cos 3.x)…

A: we have to find the derivative of the function y=(cosh x)x2

Q: ey sin x = x + xY %3D

A: Solution:- The given implicit function is  ey sinx=x+xy

Q: y = cos(r) fonksiyonunun birinci mertebeden türevini z = noktasında h = olmakla 3-nokta aranokta…

A: Given function is fx=cosx. We have to evaluate the first derivative of fx=cosx at x=π2 and h=π4. The…

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

A: Differentiate both sides w.r.t. x.And for addition we can apply the derivative separately on both…

Q: (a) By using the chain rule and the derivative if x>0 (1, -1, if x< O' d (\xl) = dx | d find - (lx3…

A: Just break the mod function in two parts and easily calculate the derivative.

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Q: A jar contains 100 mL of a certain substance which, when heated to t degrees Celsius contains E(t) =…

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Q: Find the differential dy of the given function. y sec² x x² +2 dy = sec²x(x²+2)tan x-x (x²+2)² dx x

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Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

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

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Q: 2. Please find the derivative of the following: S* cos vt dt J. cos b. Scos VE dt a.

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Q: Let y=(x to the 2nd power +3) to the 2nd power . Find the differential dy when x=4 and dx=0.2…

A: Given,    y=(x2+3)2

Q: 14. Find the derivative of y = e cosz %3D A. y' = -ecosx sin z B. y' = elinx cos x C. y' = -etinx…

A: Given,y=ecosxdifferentiating both the sides w.r.t. xdydx=ddxecosxUsing chain…

Q: 7 Find (b) x siny-ycosx-y 1.

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Q: Q16// Solve the partial differential equation a²u = cot³y given that ди == x when y= and u=y when…

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

A: We have to explain of the method of proving the derivative dydx of y= U(x)V(x) where U(x)and V(x)…

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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Q: Exercises: Find the first derivative of the following: 1) y = sinh 4x 2) y = tanh (1 –3x) 3) x =…

A: 3). To find the derivative of x=cosh23t. Solution: Power rule of differentiation states that:…

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Q: i. y = cosh(2x – 1) %3D 1 j. y = arccosh H| 8

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Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

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Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: a function y= F(x) SatisFying Hhe given find differential equationand the prescribed initial…

A: First we check type of differential equation i.e. Separable differential equation       Homogeneous…

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

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