4sinx If y then the value of y' is COSX 4 tanx 4 sec2x 4 secx tanx 4 secx

Q: dy tanx (4) Find if y = (sec x)" dx %3D

A: Here, we have the given function in the form of a variable raised to the power variable. Therefore,…

Q: (cos x cos y cotx) dx - sin x sin y dy = 0. -

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Q: 19-x Evaluate ,* sin(x + y*) dy dx

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Q: y' + y tan x sin x cos With y(4) = 0

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Q: If y=sin(sinx) show that y'' +(tanx) y''+y cos2x=0

A: we have to derivate 2 times then we will get result

Q: xy sin y dAR: - 3sXs3, 0sysn SSwsiny dA= xy sin y dA =

A: Use double integration to evaluate it

Q: aluate 4e3 tan z sec2 x dx.

A:

Q: Pined dy / dxメ メ+ tan (Xり) = 0

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Q: tanx dydx 1. 1+ y? 2cscx sin y(sin x)²r'drdxdy 2.

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Q: 2 1 + x - 1 then find dy when – 1<x <1. If y = tan dx

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Q: (2y cos y - x secy-x tan y)dy = (1 + sin y) dx

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Q: Find y' i. y = sin(2x² + tan(6x² – x)) ii. y = sin(2x² + tan(x – 1))

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Q: Let -1 y = tan' 3x2 – 1 dy Then dx

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Q: If tan(xy) = x, what is ? dx dy cos² (xy) dy 1-y tan(xy) sec(xy) dx dx x tan(xy) sec(xy) O Option 2…

A: Please refer the attached image for complete solution.

Q: find dy/dx 27. y = 4 tan (x3/3)         28. y = sec (x2 - 1)

A: ddx4tanx33Take the constant out:  a·f'=a·f '=4ddxtanx33Apply chain rule:=sec2x33ddxx33=4sec2x33x2

Q: d cos 2x – x³ i. dx 3 + tanh x

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Q: cosxdx 17. - secx+ tan x [2sin(3x)cos(5x)dx 18. [(sin y +2cos y)'dy 19. 20. ſcot'(2x)dx 21. (sin“…

A: solution is given below

Q: sec 2x cos y dx + (cos 2x + cos 2x cot2 y) dy = 0 ans: tan 2x + 2 In |csc y - cot y| = c

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Q: a) Find for 5x² – x³ sin y + 5e*y = 10 dx

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Q: dy If y= sin(sin x), then dx o cos x cos(sin x) o cos(sin x) O cos 3x cos-(sin x)

A: Solve the following

Q: if y=tanx=sinx/cosx then find dy/dx

A: Given,

Q: (÷) – -, y (1) = 1 y tan-! y'= '() x tan-!

A: We will find out the required solution.

Q: find dy/dx. y = 4/cos x + 1/tan x

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Q: 2/ Find dy To y=sin h'(tanx) 2-y (X+1)}

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Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

Q: (cos x cos y cotx) dx - sin x sin y dy = 0 -

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Q: Let 6 sin x + 7 cos y = 7. dy (6cos(x)csc(y))/7 dx dy = dx2

A: Simply take the derivative of the whole expression with respect to x than simplify.

Q: Find dy/dx tan(x-y)=y/(1+x^2)

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Q: | sec 2x tan 2x dx

A: ∫ sec2x tan2xdx=let u=2x     dudx=ddx2x    dudx=2dx=12du ∫ sec2xtan2xdx=∫ secutanu 12du∫…

Q: d'y +2 sin y cos' y = 0. dx 6. If y= tanx, show that

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Q: I3Jsin'x cos x dx .6,

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Q: dy\dx = secx tanx If, y=sec(x) Then y' = sec(x)tan(x)

A: Given that, y = sec x Let y = f(x) We have to prove that, y' = sec x tan x

Q: 2. f(x) = -7 tanx 3. y = 2 cscx 4. y= 4x cos x

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Q: Find for y = tan(x) dy dz2

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Q: find dy y = tan-1(ex2)

A: The given equation is y=tan-1ex2. To find the value of dydx. Solution: y=tan-1ex2 differentiate with…

Q: 2tany for (secx) - tan" ()+ e° csc"(x²) dy find dx sinx

A: The given function is, secx2tany=tan-1ysinx+eycsc-1(x2) Differentiate both sides with respect to x,…

Q: 1 -dx= cosº x/2sinx 5 /tanx+=Vtanº x + C А. Vtanx+/tan5x+C 1 B. tanx +÷Vtan° x +C С. 2 2 tan x +C 1…

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Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: 7)(x+tan y) dy sin 2y dx

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Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: Find dy dx if sin(x + y) = tan(xy)

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Q: (sinx+1) (cosx+1) dy evaluate dx -If: y =

A: Use the concept for derivative of the form  y = f(x)/g(x)

Q: 3. sin x cos y dx + cos x sin y dy

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Q: FIND dy/dx FOR EACH FUNCTION. 1. y = (tanx + sinx)-3

A: 1). Given y=tanx+sinx-3. To find: dydx Solution: Power rule of differentiation states that:…

Q: dy =1+ sec' y dx If sin y = 2 sin x show that

A: Given  siny=2sinx

Q: S secs/2 (금x) tans (글x) dzx

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Q: 1.) if f(x)=xx then find f`(3) 2.) if y=tanx= sinx/cosx then find dy/dx 3.)if y=x/lnx then find y`

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: FIND dy/dx 1- tan x y= (1+X)

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Q: Find y' i.y = sin(2x² + tan(6x² – x)) ii.y = sin(2x² + tan(x – 1))

A: We have to differentiate the given functions

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.