1. Determine where f(x) = arcsin (x² – 2x) is increasing. %3D

Q: Find dy/dx by implicit differentiation   x2 + xy -y2 =4

A: Differentiate both sides with respect to x. For xy use product rule

Q: find dy/dx by implicit differentiation y2 = x/x + 1

A: To get rid of the fraction we cross multiply. Then differentiate both sides with respect to x.

Q: Find dy/dx by implicit differentiation. xy + 5x + 2x2 = 3

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Q: Find dy/dx by implicit differentiation.  y^2-xy+x^2=3

A: From the given problem:   y2-xy+x2=3   Now differentiating with respect to x.…

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: arctan x Xe fel Xaresecx d

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

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

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Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

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Q: 1) Find dy/dr by implicit differentiation. tan n'(xy"+y)= x

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Q: Find the equation of the line tangent to the graph of y = arctan (sinh(r)) at z = 0. %3!

A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

Q: Find dy/dx by implicit differentiation.

A: To find dy/dx using implicit differentiation: cosx+y=x

Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: Find dy/dx by implicit differentiation for the following.:2y2 = 5 + x/5-x

A: Given: 2y2 = 5+x5-x Now differentiate the given function we get, By using the product rule,…

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: Find dy/dx by implicit differentiation. x2 + y2 = 9

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Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

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Q: Find dy/dx by implicit differentiation. xe = x - y

A: To differentiate the given equation, we need to know the product rule and chain rule of…

Q: 3) Find the equation of the curve whose arclength from the point (4, 1) to the point (9, -1) is…

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Q: S) - aresin 2. 2 arcsin 2. is constant for 0sxs 4.

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Q: Find dy/dx by implicit differentiation. x2 + xy - y2 = 4

A: Given function is, x2+xy-y2=4.   It is implicit differentiated as follows:…

Q: 4In(Arctan x) = 1-y

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Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

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Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

A: Given: y=x2+7 then A moving point on the graph is: (x,y)=(x,x2+7) And dxdt=8 cm/sec We have to find…

Q: 2. Use implicit differentiation to find dy/dx: e"y+ In(arcsin 2y) = 3ª ln y + 5.

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

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Q: solve using variation of parameters or reduction of order. (D2 + 1) y = tan x

A: Given (D2 + 1) y = tan x

Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: find dy/dx by implicit differentiation √(xy) = 1

A: xy=1Concept: In implicit differentiation, while differentiating y, one need to use dy/dx.Product…

Q: A-The derivative is y = In sin 0 cos 0 1+2 ln 0

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Q: find dy/dx by implicit differentiation ln (x/y) = 1

A: We have to find dydx by implicit differentiation for the implicit function: lnxy=1 Implicit function…

Q: Find the arc length: f(x) = (x³ + 5)ž – log x? from x = -1 to x = 3

A: Given:          f(x)=43x3+552-logx2       from x=-1 to x=3   Arc length =∫ab1+f'(x)2dx    here a=-1…

Q: find dy/dx by implicit differentiation for: f(x)=In (2x+1)^3/squareroof of x^2+1

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Q: Find dy/dx by implicit differentiation. x2y + y2x = −2

A: Given multivariable equation,  x2y + y2x = −2 To find dy/dx using implicit differentiation.

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

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Q: Find dy/dx by implicit differentiation. tan(x - y) = -Y 1 + x2

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Q: 1. S =dx = -Arcsin x√x²-4x-1 +2 X √5 +c

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + xy = 3 at x = 1 4- y…

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Q: Find dy/dx by implicit differentiation

A: Given function

Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

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Q: Compute: d/dx(arctan(2x))

A: Given

Q: find dy/dx by implicit differentiation xy = √2

A: Steps to solve implicit function using implicit differentiation Step 1: Differentiate the function…

Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

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Q: Find y' of y= In(tanh2x)

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Q: Determine the equation of the tangent line to the x³ + ln x graph of f(x) = sil 3 3 + 5tº dt at x =…

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Q: i need step by step explanations, please. Thank you.

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Q: Find dy/dx y=(x-1)(2x-x2)1/2+Arcsin(x-1)

A: y=x-12x-x2+sin-1x-1 We need to find dydx

Q: alue of A can be calculated based on f(x)dx = 1.

A: The given probability distribution function is,

Q: Find the slope of the graph of cos(x + y) = 2x at the point ( 0, T1/2 ). Hint: Differentiate…

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