Choose the Correct answer for the following: dy 1- dx for y - sech' x is equal to: a) sech x tanh x b) 3sech sech tanh x c)-3sech2x sechx tanhx

Q: Find the derivative of fl6)-32" ). (v²+5) tan (5x

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Q: 8. y = sec3 (x³ + 3) + x 9. y = cot·1Vx²- 2x

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Q: need help with correct answer

A: Step 1:The provided function is:y=(4−x7)6   .........(1)Let's claim that, f(u)=u6 and g(x)=4−x7Then,…

Q: Differentiate y = tanh 2x + coth x A. 2 B. 2 (tanh 2x) C. 2 (sech22x + csch²2x) D. 2 (sech2x –…

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Q: 7. Let y = tan (3x - 2), find y'.

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Q: 5. Find the following derivatives: a) y = x?e-2/x b) y = t tan -t- t -Int

A: Given:  5)a) y=x2e-2xb) y=ttan-1t-12lnt To find: Derivatives of the given functon.

Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: Find the derivative of y. 30) y- In (sinh 9x) 1. B) sinh 9x A) coth 9x C) 9 csch 9x D) 9 coth 9x

A: Derivative

Q: IV. Implicit differentiation 1. xy + y? = 1, find y? 2. x²y – xy? + x² + y² = 0, find y' 3. x? – xy…

A: Given: 1.xy+y2=1 , 2. x2y-xy2+x2+y2=0 3. x2-xy+y2=3 4. x3y+xy2=3 and x=1

Q: Differentiate: y = 4x - 6 Answer: y' (x)

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Q: dy for the following implicit functions : dx Find a) x+4xア-ア 5y =3 3べ+5y'x"+4\」 (ans.: 2.x 10xy-y

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Q: FIHD THE DERIVATIVE OF THE GIVEM. FUMCTION Cos? x 1-) g(x) = 2)f(x)= Sinメ tany Sinx tan y sec x Cot…

A: topic - derivatives

Q: Question: Find the derivative. y = 2tan?r – sec?r. Select one: O y' = 2sec2I tan r O y' = 4secI tan…

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Q: 5) y= 4x + x- 5x Find dx d'y dy 6) y=-2r – 4x* + 2r Find dx |

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Q: dy for the following functions: dx EX-9- Find ) y= sec'x– tan' x %3D

A: t differentiate

Q: Calculate the Derivative k (u) = arc sec(u) 3u + 2

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Q: b)g(x)= In(7x' +x° +5)

A: The given function is gx=ln7x4+x2+5 Differentiate the above expression…

Q: Calculate y' given y below. (a) xey = y − 1. (b) y = (cos x)^x (c) y =(√sin^3(√2x))

A: a). Differentiate separately both sides of the equation (treat y as a function of…

Q: Find the equation of the line that is tangent to y = 2log3(x + 1) and is perpendicular to the line y…

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Q: 25) y= Arctansinh x

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Q: Let z = CSC y y³ Then dz dy csc (y) — csc (y) [1³] X

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Q: Solve by definition of derivative if f(x)=x+Vx AND also Find x? w.r.t x*

A: fx=x+x Now by the definition of derivative, we have…

Q: 2. (y² +2) d = 5y, given y dy = dx 1 when x = HIN 2

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Q: lim (sin 2x-sinx)= sin x 26. %D A 0. B -3. C 2. Đ 1.

A: To find the given limit, limx→0sin2x-sinxsinx Using the trigonometric identity, sin2x=2sinx.cosx…

Q: Q12. If fla)= tann- 3 secu find f'(a) = find f'E) =

A: first derivative of f(x) is f'(x)= cos x+3sinx

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.