@ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

Q: If x? + y2 = 100 and dy/dt = 9, find dx/dt when y = 8. (Enter your answers as a comma-separated…

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Q: Assume x and y arefunctions of t. Evaluate dy/dx for the following.  y3=2x3+88;   dx/dt=3,     x=4,…

A: Given, y3=2x3+88dxdt=3x=4, y=6

Q: dy xe dx to

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Q: dy Differentiate implicitly to find dx 8x? + 9xy + 7y + 17y -8 = 0 dy %3D dx

A: Given query is to find the derivative of the expression.

Q: If the substitution u = x/2 is made, the integral 1-(플)2 dx = %3D -

A: Let's integrate.

Q: Use Fubini's Theorem to evaluate .2 -dx dy. I + xy

A: Given :            ∫02∫01 x1+xy dxdy By Fubini's theorem, the above integral can be rewritten as ∫01…

Q: dy Find given 3xy = In x. %3D dx

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Q: Exercise: Answer the following by finding dy/dx. 5sin-1 # – cosh x (a) y = Vsec4 x + In 7 4 (b) + In…

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Q: -1 dy find dx If y = %3D (1-VE)

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Q: Use this equation to find dy/dx. 5y cos(x) = x2 + y2 %3D dy dx %3D

A: We have, Here, we'll take derivative on both side and then isolate the dy/dx.   It is known that,

Q: evalua te the integra x?4 dx Conve or D-

A: The given integral is ∫x2-4xdx. Apply trigonometric substitution: x=2secu⇒dx=2secutanudu Now,…

Q: Find dy. (5-/x) %3D dy =| dx %3D

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Q: dy is : If x- y 0, then %3D dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 3. Linear DE of Order one 2y(у? — х)dy %3D dx

A: Linear equation of dx/dy form is made

Q: :Use variation of parameters to solve dx Зх — Зу + 4 dt dy 3D 2х — 2у — 1 dt

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Q: Exercise 4: Integrate the following. dx (a) /= 16 х dr (b) / 5 + 2x4 et dx (c) / 1+ 2e2x cot x (d)…

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Q: Evaluate LSIT (*+y+z)dx dy dz . X-Z

A: Introduction :We have to solve given triple integration .

Q: Use this information to evaluate 1 (1- e)| dx %3D x=1 et - 1

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Q: g=ズ, a find dy dx %3D

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Q: d Evaluate In(et – t²)dt. Briefly explain your answer. dx '1

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Q: (a) dy Given 4 sin 3x + 2exy = (2x + y)³, find dx'

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Q: Rewrite using the order dy dz dx. [L² dz dy dx = 5 5. O dy dz dx

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Q: dy Find , if dx y = 3u – 2 and u = 2x² - 4. dy Preview dx

A: Topic = Derivative

Q: da dy at z = – 5 if y = 3x2 – 3 and - 1. Find at x = %3D - dt dt dx %3D dt ||

A: given y=3x2-3 ........(1)

Q: dz res find z= sin dx'

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Q: Bslve the differemial egution :- rential qution: dy =y? Cos -2X"y² %3D dx

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Q: a dy Find given y = 4 In da

A: The given function,   y=4x lnx

Q: dy — х) %3D У(у + x) 2 - х(у dx

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Q: dy Find for y = cosx(1 + cscx) dx %3D

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Q: dy Differentiate implicitly to find dx 2x+7xy + 9y + 19y- 8 = 0 + dy %3D dx

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Q: Find dx/dt. Since x + y =225, then %3D 2x dx + at 2y.dy =D0 %3D This Simplifies to dx = dt dy %3D

A: Given: x2+y2=225 To Find: dxdt

Q: dy Given that y = In 9x, find dx dy dx

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Q: Is this 2-form exact? w = x dx A dy

A: Given that ω=xdx∧dy To check this  2-form is  exact or not.

Q: dy What is the value of dx at the point (1,0) if y = In(x² + y²)? %3D Undefined O 1 O 2

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Q: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as

Q: dy Differentiate implicitly to find dx 5 3 5 ху 2 2 Xy + 6x¯ = 8y +7 %3D

A: Given equation is x3y5+6x52=8y52+7. Compute the implicit derivative.…

Q: dy if x = In(csc y +c dx Calculate

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Q: Find dy/dx: (a). y = cos 8x + sin r2, (b). y = Vcos 8x + sin x². %3D

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Q: dy In y ,if cot6x - 2x'y+ xe' = 20cos2y– dx Find

A: We have to find dydx, if cot6x-2x3y+xey=20cos2y-lny2.

Q: dy 40. dx = VT/2 2ху 3D 1, у(0) 3D

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Q: Use loganthmlc differentlation to find dy/dx. y = x, dy

A: The given function,      y=xx-2, x>0

Q: dy Find if y = In|9 + x|. dx

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Q: file the loiIOwing using the ina egration and 7 0 8x +8 || dy dx dz in the order dz dx dy 0 -1 0

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Q: Find dy/dx, given that xy^3 -3y^2 +xy=1-3x

A: The main objective to calculate the derivative of the function xy3-3y2+xy=1-3x.

Q: dy y(ln y- In a +1) %3D dx

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Q: Find dy/dx: 1. у%3D Jo = San* sec? t dt

A: A detailed solution is given below

Q: dy find 3 - x x - 2 1) If y = t + 2t , t = %3D %3D dx

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

Q: Calculate dy/dx You need not expand your answer y=(x+5)( x2 - 5) dy/dy=

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