find dy/dx 19) y=Sin" (5x' ) 24) y= Sin 2x.Cos2x 42) y = sinh (tan x)

Q: dx (2) S V9-x² E(Ctrl) X. 2x sin-1(구)+ sin-1 (민 + Option 1 Option 2 2x cos-1(민 + c CoS Option 3

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Q: Find the intergration of x^3(x^4-sine)^5 dx

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Q: Integrate: S sin3x cos²x dx

A: The given integral is ∫sin3xcos2xdx

Q: Find the first derivative of  y = (x – 1) √ (2x – x2)   + arcsin (x – 1), and y = arctan [ (3 sin x)…

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Q: 6. Find dy/dx by implicit differentiation for tan-'(²y) = sin(x²) + 3ry?.

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Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: If y=(sin3x-cos3x)², find dy dx

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Q: 1) [(sinh 2x + cosh2x)° dx

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Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

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Q: Find the derivative of y=cos4 x sin4 x Ans: 1/2 sin3 (2x) cos cos (2x) solution?

A: We simplify the given expression using the double angle property

Q: 3) еУsinx dx %— cos²x dy

A: Differential equation

Q: - sinx) dx 2. 1. (COSX (ax' +b)*x dx 2. 2/3

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Q: find dy/dx of y=cos2x-sin4x

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Q: sin x (cos x+1) dx 7. S (cosx +1)2

A: Given that: ∫sinx(cosx+1)(cosx+1)2dx           NOTE: As per our answering guidelines, we can only…

Q: = sin(5x) for y(0) = 2

A: the solution is, y = (11 - cos5x)/5  The detailed solution is as follows below:

Q: Find dy/dx of y=sin-(1/,). 9x-

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Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: solve for the intergral of (2sinx)/(1+cos^2x)dx

A: The integral to be evaluated is  ∫2 sinx1+cos2xdx. Here, we can use substitution method to evaluate…

Q: find dy/dx (sin2x)x

A: Explanation of the answer is as follows

Q: Integrate  dy/dx sinx=1

A: We know, ddxcosec x = -cosec x·cot x ddxcot x=-cosec2x ddx(cosec x-cot x)=-cosec x·cot x + cosec2x…

Q: 5. 2x sinh+ 3y cosh2) dx -- 3x cosh dy = 0

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Q: Show that d /dx  arctan ( tanh x ) = sech 2x

A: We have to show that ddx(tan-1tanhx)=sech2x

Q: Integrate: x² cos(2x) dx

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Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: 2.Find , if y = sinh x %3D dx' 1+cosh x

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Q: 2. Integrate using Trig: cos° x dx

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Q: Determine dy/dx given that: y = sinx - sin³ x O cos³x O cos x sin² x O sin³ x O - cos³ x -

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Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: 5. Find where y = In(cosh(2x)) + /sinh-1(2x) + tanh² (7x). dy dx

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Q: = Solve: Cony siny dx + dy. cosr sinx

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Q: 2T sin (2) dydx 0,

A: To evaluate the double integral, ∫π2π∫0x3sinyxdydx.…

Q: 3- - 플 플 sin²cyl y จน

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Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: Find dy/dx by implicit differentiation 4 cos (7r) sin (6y ) 5

A: We have been given an implicit function and we are supposed to find dy/dx.

Q: Find dy/dx 1. y = sin ( 5x - 9) 2. y = sin-4x/5

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Q: Find dy/dx of x siny + y = 4x + 3

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Q: - y = sin² (3*)

A: We have to find derivative of given function.

Q: 1- Sinx + Cos2y=0 dy dx

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: solve  sin(x)dy/dx + ycos(x) = cos(x)[ex + sec2(x)].

A: Convert into dy/dx+p(x) y=Q(x)

Q: х2 9 dy + sinx - у %3D0 dx

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Q: Find dy/dx by implicit differentiation. (cos TX + sin ny)³ = 26 dy/dx =

A: Differentiate above equation with respect to x

Q: Find dy/dx by implicit differentiation   4Sin (x2) =x Sin (y2)

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Q: Integrate: S dx sin ³x cos6x

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Q: Find dx if 2 siny dy 3 Log (y1)

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Q: 2 sinºx cos®x dx

A: here we use integration method, as we seen that the power of the sin and cos are even . so we use…

Q: Find dy/dx at (-4,1) if xy=(8y/(x+2)). dy/dx at (-4,1) =?

A: Derivative of any function determines the rate of change of a function. It is represented as dydx if…

Q: 29. (csc x – sec x)(sin x + cos x) dx find + In 5 ) dx 30. 3 sinh .3 2x3 V1 + x² sin x dx 32. 31. dx…

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Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: Given: cosx+tanxy+4=3We need to find dydx.Recall the formulas: ddxcosx=-sinx…

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.