f(x, y) dx dy = f(x, v) dy dx

Q: dy x +1 xy %3D dx

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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 if y = e-et dx Find %3D dy %3D dx

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Q: Let y = = 1/2 √ √x. Then evx dy dx is:

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Q: Find dx/dt given that 4x^2+9y^2=13x  x=1,  y=-1 and dy/dt = 10

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Q: dy Find at x = dt dy dt || 4 if y = 3x² + 5 and dx dt = 1.

A: Let's find dy/dt value at x=4.

Q: dx If y = 2x3 + 3x and dt dy 3, find when x = 4. %3D dt dy dt =

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Q: Find dy/dx. X=sec(t), y=tan(t); t= 3 dy dy 2 а. с. dx 33 dx 3 dy b. dx 3 dy d. 3 dx 33

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Q: Assume that y=2x and dx/dt =4. Find dy/dt . dy/dt

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Q: find both dy/dx (treating y as a differentiablefunction of x) and dx/dy (treating x as a…

A: Differentiating with respect to x, we get

Q: 3 хy dx dy 1

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Q: Find the integrating factor of x dy / dx =x^ 2 +3y,

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Q: dx dy + y = x , dt = 3y dt dx dy 1.

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Q: Find dy/dt. y = tan x; dx/dt = 3, x =π/4

A: Consider the following function:        y=tanx finddydt when dxdt=3,x=π/4.

Q: f(x, y, z) dx dz dy f(x, y, z) dy dx dz f(x, y, z) dy dz dx

A: Given ∫064∫x8∫08-yfx,y,zdzdydx So, limits of x from 0 to 64 limit of y is from  x to 8  limit of z…

Q: Find f. fy for f(x,y) = xcosy + %3D x5 siny3 ey

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Q: dy at x = 1 if y = 4x² + 1 and dt dx Find – 1. dt dy dt || ||

A: Solve the following derivative

Q: Find dy/dx in terms of a and y if aty – x- 2y- 2 = 0. dy %3D dx

A: It is implicit  derivative.

Q: dx at x = dt dy Find - 5 if y = x² - 3 and = 4. dt

A: A detailed solution is given below

Q: Find of / dx and of / dy. f(x,y) = e(x+ y + 9) of / dx = df / dy =

A: Let f be a function of x and y. The expression ∂f∂x implies that partial derivative of f with…

Q: find both dy/dx (treating y as a differentiablefunction of x) and dx/dy (treating x as a…

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Q: Find dy. y= 2 In (3+x*) dy =|

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Q: dx at x = dt dy - 22 – 2 and dt – 5 if y = 4. Find - dx dt

A: We will find the derivative.

Q: Xyz f(x.y.z) = function is given dt P(2,t,) in point fax + fy + f2z colculate.

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Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: Find of / dx and of /ay. f(x.y) = elx +y+6) of I dx = of I dy =

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Q: Assume that y = 5x and dx/dt = 2. Find dy/dt.

A: Consider y = 5xApplying derivative with respect to t on both sides and plugging the values:

Q: dy at x = dt dx Find - 4 if y = 4x² +1 and -2. %3D dt dy %3D dt

A: Take the derivative with respect to t and put the given values.

Q: Find the differential dy. y = ex/2   dy=

A: Here the given expression is y = ex/2. Apply the chain rule:

Q: dy — х) %3D У(у + x) 2 - х(у dx

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Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

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Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

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Q: dy/dx=x3cosy

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Q: Find dy/dx. x = 9/t, , y = Vte-t

A: topic - derivative

Q: Find the integrating factor of y(2x - y + 1)dx + x(3x – 4y + 3)dy = 0 Oy? 2x О ху Oy

A: See the details solution in below

Q: y = x*, d'y 1 dy dx y dx, Prove that Y = 0. X

A: First we find out dy/dx then d2y/dx2. And put the values of dy/dx and d2y/dx2 in given condition.

Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: dy Find dx by implicit differentiation. 3 +y = 25 -1 dy 9x а. dx 4y dy b. dx 4x Зу -1 dy 4х с. dx 1…

A: We need to find dydx of x23+y32=25. So,                 x23+y32=25Differentiating both sides wrt…

Q: dy Find using partial derivatives. dx sin(x + y) + cos(x - y) = 9 dy %3D dx

A: Given,

Q: (sin y — y sin х)dx + (сosx + хcos y — у)dy %3D 0

A: Given differential equation is,  (siny-ysinx)dx +( cosx +xcosy -y)dy=0 comparing the given equation…

Q: 9. dx/dt = −(x − y)(6 — x − y), dy/dt=x(4+y)

A: Given that, dxdt=-x-y6-x-ydydt=x4+y We have to determine all critical points of the system of…

Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: Show that f(x.y) dy dx= ,f(x,y) dx dy. ||

A: Order of change of integrals

Q: Find dy/dx by implicit differentiation. V xy = 6 + x²y %3D dy dx

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Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: y.cos(z) dx dy dz * 0 0

A: Given that: ∫01∫0π∫0πy.coszdxdydz

Q: dy dx at x = dt Find 2 if y = – 5x² + 5 and = 1. - dt dx dt

A: Here we use the derivative formula. find dy/dx  there after we will use chain rule -. dy/dx =…

Q: Find of/ dx and of /dy. f(x,y)= e(x+y+ 4) of/ dx = %3D of / dy %3D

A: