dy Find for the following functions: d.x (i) y = 5sin(3z²) (ii) y = ezVz² +1 (iii) y = (tanh-' (V#² – 1))*. (iv) y = sin-(sin x).

Q: y=8sin(x)cos(x) ; x=pi/3

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Q: If 5 cos x +3y = 4 then using the implicit differentiation we have Select one: dy 5 sin x %3D dx 9y2…

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Q: Find the first derivative: y = In sin e Oy = 2e sece Oy = -2e cot e= Oy = 2e tane Oy = 2e cscez

A: Solve by derivation

Q: 3. Find y' for y= cos(sin² x) 4. If x=y√/1-y², find y dx

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Q: Q3) Find dy/dx if 1- y= In x 2- y=x sinx+1-x

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Q: 7) Find dx 4e* dy if y = %3D 8) Find the first derivative of f (x) = sin? (x°).

A: We need to find out : 7)  dydx if y=4exx 8) First derivative of f(x)=sin2(x3)

Q: Find dy/dx at x=0 if y= Cosu and y--3x

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Q: 2- X. Sin (5X) dx: Cos (SX) X Sin (SX), Cos (SX) XSin (SX) XSin (SX) Cos (SX) 25 25 25

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Q: I. Find an equation of the tangent line to the graph of t cosh (f² – 1) dt tan-l † | f(x)%3D /1+ln…

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Q: Compute dy/dx if sin(x) = cos(xy^2

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Q: That question please

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Q: dy/dx of y = (x^2)cos^4(x)

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Q: 1. Find dy/dx which x = -1 y = 1/x arc tan 1/x  2. Find dy/dx which x = 1/e y= arc tan (ln x)

A: 1. Find dy/dx which x = -1, y = 1/x arc tan 1/x  Differentiating y with respect to x.  Since y is a…

Q: Bind dy, 4. Ssinx.cosx sinx-coSX 1 +2.Ln X

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Q: Compute dy/dx for the function. 2. y sinh - 6x

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Q: Find dy if y = tanh-1(5x²) csch¬'(In x). dx

A: Given: y=tanh-1(5x2)csch-1(lnx)To find:dydx=

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: x(1- siny)dy = (cosx cosx – cosy -y)dx. 0.

A: The given differential equation is x1-sinydy =cosx-cosy-ydxyπ2=0

Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

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Q: followin COSX 3. f- dx 1+sinx 4. f (sinx + cos x)² dx 203 (y² +1) 20 dy 5. f

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x day 6. dx if y = 1-cos4x 1+cos4x dx² dy 7. a if y = In…

A: (7) Let y=lnsinh 5θ and x=cosh(4θ)

Q: dy Find by implicit differentiation. dz 3+ 5z = sin(ry) dy

A: We can find the answer using implicit differentiation as below.

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: Find the second derivative 1. y = In(x^3+1) 2. y = Arctan (e^x)

A: Given: y=lnx3+1, y=tan-1ex

Q: (5) Find the derivative dy/dx, where: 4 1 -1 y=- y = cosec(cot3x), y=Vsinh¯3x 3 1+ cos° x

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: Compute dy/dx for the function. 5) y = In sinh 6x

A: topic- derivative of a function

Q: Find dy/dx by implicit differentiation: sinx=x(1+tany)

A: We have to find the dydx of the function by implicit differentiation.

Q: Let y = tan(4x + 3). Find the differential dy when x = 3 and dx = 0.3 Find the differential dy when…

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Q: dy Find at x=0: dx y = (In(cos "x*) -1 COS sinh x %3D

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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: ey sin x = x + xY %3D

A: Solution:- The given implicit function is  ey sinx=x+xy

Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: dy =Cos x Sinx cotX 8-

A: As we know that; The standard form of the linear differential equation; dydx+Py=Q Where P & Q is…

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

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

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Q: sin(2x) dx+cos(3y) dy=0,y(π/2)=π/3

A: Consider the provided differential equation with given initial condition,

Q: Find dy/dx by implicit differentiation. 5y sin(x2) = 9x sin(y2)

A: Given :  5y sin (x2) = 9x sin (y2)

Q: 5) sinh(x)cos(y)dx = cosh(x)sin(y)dy

A: A differential equation (Mdx+Ndy=0) is exact if  dM/dy= dN/dx

Q: dy dx by implicit differentiation. 9. Find sinx +Scos 3y = 4

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

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

A: These problems can be solved by the application of Chain rule.

Q: how do i implicitly differentiate (solve for dy/dx) where: xy = tan(xy)?

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Q: Find dy/dx of sin^2(3y)=x+y at (2 - pi)/4 , pi/4

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Q: The derivative of y = In(sin(ex + 1)) is O y' = -ex cot(ex + 1) the above y' = -ex tan(ex + 1)

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Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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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…

Q: Find (dy/dx) for: tan-¹(x + y) + In(x³y) = sinh(y)

A: To find dydx for: tan-1x+y+lnx3y=πsinhy

Q: Find dy/dx by implicit differentiation. 5x^(3)+x^(2)y-xy^(3)=-8 dy/dx=?

A: We are given an implicit equation as