@Hiw/ prove that cosiz=coshz @ Cosh'z -sinh'z=1 @1-Tanhz Sechz D cos hiz-l = cschz COS 3 =- Sinh z sinh (-2) Cosh(-2)=cosha

Q: y' + y tan x = sin 2x cos³ x y3 given x=0, y=1

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Q: to find the implicit differentiation Use dy of *y'+tsiny =4

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Q: Find the derivative of the function. y = sin-(6x + 1) y' =

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Q: dx/dt of -ln(-cos t)-e^(sin t)

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Q: sin' xcos* x dx x cos

A: Perform integration

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Q: (b) y = e=* + + In(3z + 1) (c) y = (cos z)° + sin(2*) (d) y = #° arcsin(2*)

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Q: Consider a function f(x) where f" (x) = 2ª (ln 2)² + sin(-. -). 2 a) Find / f"(x) dæ. b) Assume that…

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Q: i.y = sin-1 (x), y € - ii.y = cos-1 (x), y € [0,¤] iii.y = tan-1 (x), y € (- 2'2 (x), y € [-;, 2'2

A: To prove the derivative formula for inverse trigonometry function we keeo the equation in terms of x…

Q: f) y= xcos(xln x) g) y= 3(sin 2x – x* }** In. 3x'e** h) y= cosx

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Q: @ sin (cos' ( )

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: Let y=f(x)=sin^2(x)-cos(x)+2sin(x)+x find f'(x), factor f'(x) and determine the critcal values on…

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Q: Find derivative A) y=sin x/1-cos x B) p(x)= 3/1+10e^4x Simplify answer

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Q: Differentiate y = In ( sin² (4x)). A y' = 8 tan (4x) y' = 8 cot (4x) y' = 8 csc2 (4x) sin (8x) y' =…

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Q: Solve for the derivative Arc sin + Arc cos =0 y y

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Q: tan°(x) sec²(x) dx = 1/7tan^7(x)+1/9tan^9(x) %3D

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Q: b) Find the derivative of the following: √cos³ (2x+1) (In(sin(2x+1)))² 1. dx

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Q: The derivative of the function y = ecos²(x) is: y' = - sin(2x)eCos² (x) y' = sin(2x)eCos²(x) the…

A: We will find the derivatives of the given function y=ecos2x in the following step.

Q: y= sinh(2n)-글교 dy/dx gi

A: Derivative of sinx is cosx.

Q: d Find dx 3 sin(x) + Vx + arctan (x³)

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Q: 9) | sin´x-cos'x dx 10) [ cor"/x - dx

A: Solve: 9)  ∫sin4xcos3xdx10) ∫cot2xxdx

Q: The derivative of y= sech-1(x sechx)+e$inh (Inx) equals Select one: – x sechx tanhx+ sechx O y:…

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Q: 5, Find derivative y = Cott-tanx

A: We will find the derivative as following.

Q: @ Find an equation of the tangent line to the curv@ x² + y² + xy = 16 at the point (0, 2). 4 b) Find…

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Q: d If n is a positive integer, one can show that (sin" x cos nx) : appropriate differentiation rules…

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Q: 25) y= Arctansinh x

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.