2. Prove the formula of the derivative of y = cosec-f(x). d²y and dx2 of the parametric equation x(t) = sech2(t), y(t) = tanh (t). 3. Find %3D %3D dx 4. A closed cylindrical can is made to hold a volume of 340 ml. What are the dimensions that wil minimize the cost of metal to manufacture the can?

Q: 18. y = x/I - x?

A: Differentiation:- The derivative of a function of real variable measures the sensitivity to change…

Q: 2. Consider y = cos(2x). 2.1. Find Y dx 2.2. Determine an equation for the tangent line at x 0.

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Q: Can you help me with this problem step by step?

A: Given:

Q: Find the dy/dx by implicit differentiation. 1. 4x2 – 9y2 = 1 2. x³ + y3 = 8xy 3. x? – 7xy + y2 = 0 |

A: As we know that; The sum/difference rule: f±g'=f'±g' The Power law; ddxxn=nxn-1 The Product rule:…

Q: can any thing said about the tengent to the curves y=sinmx and y= - sin(x/m) at the origion (ma…

A: Solution  Given

Q: If the equilibrium of dy/dx = y - sqrt(y) when y>0 is y=1, is it a stable or unstable equilibrium?

A: Given dydx=y−y, when y>0 We have to check whether y=1 is stable or unstable equilibrium. Note:-…

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: -2r²+2x+1 ev dy at x = 0. Find the equation of the tangent line to the graph of F(x) = sech z

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy dy Find the first…

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Q: . Suppose y is a function of x defined implicitly by sin y + y = x²y² + In(x) – 1 Find dy/dx and…

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Q: Find the derivative of y with respect to 0. y = In (8 cos 2e) dy %3D de

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Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: 2. Calculate the derivative dy for the parametric equation x = t² + ³ + ln(4t+1), y=e5t² giving your…

A:

Q: 14) find the respect of y with respect to x Y=(6x+5)^x dy/dx=?

A: Given function: y=6x+5x Taking log to the both sides logy=log6x+5x We know that logxa=a log(x) So,…

Q: fy = f(r), how do we define the differential dy

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Q: Can you help me with this problem step by step?

A: The given equation is x = cot y.Differentiate both sides with respect to x.

Q: Find the differential dy of the given function. y = arctan(x - 2) dy dx

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Q: 9. Find dy for y defined implicitly. by the equation xy-secly)-3x

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Q: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

A: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

Q: 1. Solve for y of the Separable D.E. sinx dx +y dy = 0

A: To solve the given differential equation for y.

Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

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Q: Find the differential dy of the given function. y = sec2x/(x2 + 1)

A:

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: Find the differential dy of the given function. dy sec x x² +9

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Q: 30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2)…

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Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

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Q: H. \ || 20 s s sec (cosx) dy dx siny 3y steb e dx dy >+

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let y = tan(2x +5). Find the differential dy when x 3 and dr = 0.1 Find the differential dy when z =…

A: Given that y=tan(2x+5) find the differential dy when x=3 and dx=0.1 find the differential dy when…

Q: Given that xyt – 6 = 0, find dy by implicit differentiation. - %3D dx? dy dx?

A: A detailed solution is given below

Q: 19. State the order and degree of the differential d y d³y equation dx dy Cosx dx +2 + dx? а. 3, 2…

A: Order of the differential equation The highest derivative in the differential equation is the order…

Q: Find the differential dy of the given function.    y = x tan x

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Q: 10. use "Bernoull's Equation" method dy -y= ey! dx

A: The given problem is to solve the Ordinary differential equation using Bernoulli equation method, we…

Q: (3) Let 4 = x²y² + x sin y, find 2 dy in terms of x and y; dx (4) Find the equation of the tangent…

A: For the given problem, there are two questions. But according to rules of Bartleby only the first…

Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: 8. Find dy/dx in terms of x and y using implicit differentiaton 5y 4 +x 2 = 9

A: Step for implicit differentiation: (1) Differentiate with respect to x (2) Collect all the…

Q: Show every detail of your solution. Differential equatioens. siny dx + (x - sin? y)dy3D0

A: The given differential equation is: sin y dx+(x-sin2y)dy=0⇒sin y dx=-(x-sin2y)dy⇒dxdy=-(x-sin2y)sin…

Q: Find dy/dx by Implicit differentiation. x = 7 In(y-24), (0, 5) dy %3D dx Find the slope of the graph…

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Q: Find the differential dy of the given function. Y=x+1/3x-2 Dy=?

A: Given, y=x+13x-2

Q: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

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Q: Hw #4 ( 2 xy +y -tany) dx+(x²-x tany tSeiy )dy =o ??

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = arctan(x – 2) dy = ||

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Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: 2 Calculate the (d^n*y)/(dx^n) derivative of the curve with the parametric equation x=lnt, y=t^alpha

A: The given problem is to find the nth derivative of y with respect to x of the given parametric…

Q: Find the differential dy of the given function. y = √(9 − x2)

A: The given function is Now, find the derivative of the function

Q: Solve the differential equatic y' = (x + y + 2)², Chart Area y(0) = 2 by setting u = x + y + 2.

A: y'=x+y+22let u=x+y+2     u'=1+y'     y'=u'-1

Q: 2. Find the linear approximation to y = sinh (3x) at x=2. State your answer in both exact form and…

A: Find the linear approximation of f(x) at a point x=2

Q: Let y = tan(3x + 5). Find the differential dy when a = 4 and dæ = 0.1 Find the differential dy when…

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Q: Let y tan(3x + 2). Find the differential dy when x = 4 and dæ 0.2 Find the differential dy when a =…

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