1. y=sech (2x-1) 2. y=(x² -1) tanh

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

A:

Q: Find y′ if y = tanh−1(sinh x2).

A:

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

A:

Q: Find the particular solution for: y' sin(2y) - cosx = 0, x =when y = 0 %3D 2

A:

Q: ЗсoshЗx dx| 4 + sinh3x 1/3

A: Given: 13∫3cosh3x4+sinh3xdx

Q: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

A:

Q: and dr= %3D Solve for the differential of y When y=sinxx x

A:

Q: sec( c)+y dy e sec do

A: Given differential equation is homogeneous equation

Q: 1) ex-ydx + sin y sec x dy = 0

A:

Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

A:

Q: 3) y sin-ly² dy

A:

Q: y = sech /2 + v2x + 1 + tanh v8x² + 3

A: To find the derivative of the function

Q: 4. |1- sin2y dy 6. y +2)/y- 1) dy (y + 2)/y

A:

Q: solve for dy/dx :  arcsin (x/y) + arccos(y/x) = 5

A:

Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

A:

Q: Find dy/dx if y=(4/cosx)+(1/tanx)

A:

Q: Solve 3e* tan y dx+(1-e*)sec² y dy = 0.

A: To solve the given differenrial equation.

Q: 25. Find x, y, eR from 2coshy - 7sinhx = 3 and coshy - 3 sinh² = 2 %3D

A: The given system of equation: 2cosh(y)-7sinh(x)=3                    ......  (1)cosh(y)-3sinh(x)=2…

Q: tanx dx = -In/secx|+C^O .BO In|secx|+CO In/cscx| +CO -In|cscx|+C°O .D

A: We need to evaluate the following integral I = ∫tanxdx

Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: 2 (b) - 2y dx +(2y tan'(x )-2x +sinh (y))dy = 0

A:

Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

A:

Q: y" + 2y' = sin 2x ||

A:

Q: 2. if 2x3 +10 x?siny-y"tanx = 0 ノ the y' so dy write ex pressin in terms of X and y.

A: Applying implicit derivative we have

Q: Find y' if y= In(tanhx) +cosh-(coth2x) Select one: O y' = cothx- 2csch2x 1 O y = -2csch2x sinh x…

A: The differential of products of trigonometric functions can be calculated using the product rule.…

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

A:

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

A:

Q: Find dy/dx 1. y = x^2(sin^−1 x)^3 2. y = e^tanh x/x^2 − sechx 3. y = tan^−1 (sechx) + sech(tan^−1…

A: We expert are following guidelines.We are supposed to do first question. We have to find dy/dx

Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

A:

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

A:

Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

A:

Q: Find dy/dx y=(7x-1)tan(2x^2-x+9)

A:

Q: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

A: I am attaching image so that you understand each and every step.

Q: 57 ves y sinx and y=cosx from x=- to x=- 4 4

A:

Q: dy Exc:" of y = tanh (x5 – 5x)² --

A: Solution:Given         y=tanh4(x5-5x)2  To find dydxFormula:ddx(xn)=nxn-1ddx(tanh x)=sech2x

Q: Solve for the differential of y when y=sinxx: x=-, and dx 3 2 2 2 4

A: y=sinπx, x=13, dx=12

Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

A:

Q: 4. STT- COs y dy -COS

A: The objective of the question is evaluate the indefinite integral.

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: 4. Differentiate y with respect to x. y = (In Vcosh3x)(sinh(2x + 1) ex+1)

A: The given function is: y=lncosh (3x)sinh-1(2x+1)

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

A:

Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

A:

Q: 3e° 3ecsch 3x 11) -dx sinh 3x tanh 3x

A:

Q: Find y't yu 4=In(sec 9x +tangx)

A:

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

A:

Q: Find where where y = V5x + sech¬1 x + In (tanh(x² + 3)). dx

A:

Q: Cualuate the definle integial. x33 COs (xH) dx

A:

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.