2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

Q: Can you explain the question step by step

A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

Q: Let y = f(x), where f(x) = v 6x2 – | Find the differential of the function. dy =

A: In the question we have to find the value of differential of the function.

Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

A: 1 Given integral is ∫03∫01x2+3y2dydx. We have to evaluate the given integral  by using Simpson's 13…

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

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Q: 5. f'(x) dx = Choose... 6. cosh t dt = Choose...

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Q: Let y = f(x), where dy f(x) = = 3 Find the differential of the function. x³ + 3 3 X

A: Find the differential of function

Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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Q: dy Let y = f(x) such that In(x – y) = 2x – y + e². Find dx

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Q: Let y = f(x), where f(x) = 5x² + 5. Find the differential of the function. dy = X

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Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

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Q: Find the differential dy. y = 5x2 / x-9       dy =

A:

Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: Use the differential dy to approximate Ay when x changes from x = 2 to x = 2.04. y = V3x – 2 A. 0.01…

A: Given that: y=3x-2x=2 to x=2.04

Q: Solve for the given DE: y(y^3-x)dx+x(y^3+x)dy=0

A: first we will check this is exact or not this is not exact then we will find its integrating factor…

Q: 2, 0 1

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Q: ²+ re" = 2y + e² %3D

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Q: B. If R = xyz’i+÷j – yz*k_find of the differential R, dR.

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Q: Find dy for the given values of x and Ax. y = 3x+5; x = 1; Ax 0.24 What is the derivative of y = V3x…

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Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: Find dy if x=t+6f and y= dx 2 5 at t=1 +

A: We have to find dy/dx

Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

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Q: dF Q. IF the value of (t) change from x to x. Find the r(x.t) = (t-x) cos( F(x) = S(x,t) dt for…

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Q: Let y = f(x), where f(x) = 7x5/6 + 5x²/3. Find the differential of the function. dy = X

A: The objective is to find the differential function.

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

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Q: If f(x,y) = y2 ex + 3 ln (xy), find fxyy (1,1). fxyy (1,1) = ?

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

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Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

A:

Q: 1 dy 2 - Y = 0 y =x*prove that - 2)- = 0 y dx

A: Given, y=xxTake log on both sides,lny=lnxxlny=xlnxDifferentiate on both…

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: (ztan 2 +1) dx – x dy = 0

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Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: Find a continuous solution satisfying dy dx + 2xy = f(x) where { x if 0 < x < 1 romer 0 if x ≥ 1 ,…

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: 2 dz dz dz ds dt dz dy

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Q: 11. Integrate the function. y? dy (49 – y²) 7y y + C V49 – y2 – sin y+C -1 - V49 - y2 | O A. O B.…

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Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: B) Find Sx e2x dx, at h = 0.2, use Simpson's 1/3 rule. J0.4

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Q: of and dy For the function f(x.y) = sin (2x - 5y), find dx of of

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Q: dx Find the value of at y-1 if x-z+5z and z= dy (y? + 2y)2/3.

A: x=z3+5z  &amp;  z=y2+2y23 Now put z=y2+2y23 in x=z3+5z, we get x=y2+2y233+5y2+2y23⇒x=y2+2y2+5y2+2y23…

Q: Find the differential dy. x + 2 y = 9x - 1 dy =

A: In this question we have to find we have differentiation of y.

Q: dy Find given that dt x² + y² = 2x + 4y, x = 3 y = 1, and dy = | dt dx dt = 6

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Q: 56. Given that x+y - xy and that y dx dy when x 1 show that xy = e*

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).