If y(x) = u/v, then y' is * du Option1 Option3 du vdu Option4 Option 2

Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

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Q: Find both first partial derivatives. z = 15XVY 15xVy %3D dz az

A: We need to find partial derivative.

Q: dx/dt = 2 and y=x^3, what is dy/dt when x=-4,2,6

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Q: 2 dydx + f(x, y)dydx

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Q: A curve passes through the point (2,0) has gradient dy at point (x, y) that satisfy the dx equation…

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Q: xUx+yUy=U , U(x,1)=2+e^-x

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Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

Q: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

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Q: 37. - dy y. dt

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Q: Find the differential dy. y = 6x7 + 3x2

A: Given:y=6x7+3x2

Q: If y = 2x^2 - 3x and dy/dt = 3, find dx/dt when x=2.

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Q: y =x3 dy Itx² -

A: Note  You type wrong Question here in place of dx/dy must be dy/dx  I solve it using dy/dx otherwise…

Q: Solve for dy given xsin y - ycos x = 2 | dx sin y-ysin x А. cOS X-XCOs y sin y+ysin x В. coS X-XCOs…

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Q: Find the indicated partial derivative. f(x, y, z)=euz²; fzyz fxyz(x, y, z) =

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Q: Find both first partial derivatives. z= 4y?V dz az ду

A: We can solve the problem by partial derivative method.

Q: 2 max f (2х + и)dte dx - 5 — и?, x (0) 3D1,x(2) freet dt

A: Given: maxf=∫02(2x+u)dt dxdt=5-u2,     x(0)=1,      x(2).free

Q: Find both first partial derivatives, as well as fy for

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Q: Find both first partial derivatives. xy (x, y) = x + y? (X, v) = (X, y) -

A: Question is solved.

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: Find both first partial derivatives. . z = ln x/ y

A: Given that z=lnxy

Q: Find aff dy dx² for f(x, y) = exy

A: I have done solution in detail....step by step....go through the solution

Q: Find the indicated partial derivatives. y+ Sz az dy ex

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Q: Find the first partial derivatives of f(x,y) = 2 ex"y of II

A: Consider the given function. fx,y=2ex10y The objective of the problem is to find the first partial…

Q: 2 In sec Vi + tag V + C sec sec z dz %D

A: 35. given integral,∫sec x . dxx = 2∫sec x12 . 12x-12dxlet x12 = u⇒ 12x12-1 dx = du⇒12x-12dx = du

Q: Find both first partial derivatives. z = 4y²/x az ax az ду || ||

A: z=4y2x

Q: Find both first partial derivatives. z = 2y2√x

A: fx = differentiate with respect to xfy=differentiate with respect to yddxxn=n xn-1

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: Find all first and second partial derivatives of f(x, y) = sin(ry)

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Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: The integrating factor of Y + 3y cscx= cotx is?

A: Consider the given differential equation, y'+3ycscx=cotx This is the first order linear differential…

Q: (continue solution of de) (2ysinxcosx - y + 2y²e*Y" )dx = (x - sin²x - 4xye*y" )dy

A: Using method of exact differential equation.

Q: dy 3. y = [(x + 1)(x – 1)]³, dx dy 4. y = (t + 4)(t – 2)(t – 1), dt 12/07/2021 15:

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Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

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Q: Find the first partial derivatives of the function. f(x, y, z) = x7yz2+ 4yz

A: From the given problem:   fx,y,z=x7yz2+4yz   So,   fxx,y,z=∂f∂x=∂ ∂ xx7yz2+4yz=∂ ∂ xx7yz2+∂ ∂…

Q: 2. [ y dy dx carctan3/2 3 secx 3/2

A: Topic  = Integration

Q: Find both first partial derivatives. z = ln√xy

A: Given  z = ln√xy. We need to find both the first partial derivatives of the above function.

Q: Find both first partial derivative h(x, y) = e-(xª + y^) hx(x, y) = hy(x, y)

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Q: ion dy 3t2 dt 2y + 2t3y' tion: ||

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Q: Use integrable combination: y(2x+y^2)dx+x(y^2−x)dy=0

A: Given :y(2x+y2)dx+x(y2-x)dy=0

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: dy+チ=-

A: Note: Since you  have mentioned multiple question, I answered first problem. If you need answer of…

Q: Let y=sqrtX. Find dy/dt when x=4 and dx/dt=3

A: →Use chain rule of differentiation.→dxndx = n xn-1     When n = 12         dx12dx = 12 x12-1…

Q: If x3 + y3 = 9 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2?

A: Given,

Q: 4) dy dy dz 5) dy dy

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Q: Find both first partial derivatives. f(x, y) = 3x - 9y + 8 F,(x, y) f,lx, y) = |

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Q: Suppose a particular investor derives utility function - U(x, y) - from owning x units of stocks and…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: