Find əzləx of z = tan-1(x²y) + tan¬1(xy2). v² dz dx 1+x*y?° 1+x*y* ху 4,2 2,,4 dz 2ху 2y? Əx " 1+x*y² * 1+x*yA əx 4,2 2,4 y? 2,4 1+x*y²°1+x?y* dz о дг 2y o əz 2ху 1+ x*y?°1+x?y* 4,2 2,4

Q: 3. 5y“ y = 5y^2 4. 4x*y°m', 8xy°m', x’y´m 4 3 7 т, 5 3 т, 5.2, а, ь, с b’, c

A: LCM :  least common multiple of two or many number is known as LCM .    3.    LCM of  5 y2 , y = 5y2…

Q: Q1: Find dy for the following a) y = tan-1(sinx) + In (sec2x) + 8tan5x + etn dx b) y = sec (x') +…

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Q: y" +2y = 2x+5-e-2r y""-6y"=3-cosa

A: These questions are about ordinary differential equation.

Q: Find the derivative of y = In O O a.) dy dx =In(5) +4ln(x) —In(cosx) 4 1 dx X COSX b.) dy = c.) dy 1…

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Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: Find y SX a) y = 3 sin (x² + 5x - 3) y' = c) y = sin" (6x) y'= b) xE5X+2 d) y = In (2x) Y₁ = Y y' =

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Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

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Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

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Q: 100° |(x–10)* \(2y+24)°´ y is equal to _?

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Q: How did he get the value inside the circle f(x, y)=x² + sin(xy) Vf=x*+sin(xy)) i+ d(x²+sin(xy)), dx…

A: given ∇f(1,0)=2i+j we have to find the direction in which the directional derivative has some value.

Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: Find y" in Exercises 71-78. 71. y - (1 + 2) 72. y - (1 - vī) 73. y - cot (3x – 1) 74. y - 9 tan 75.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Hiw 2 Find dy For (πCシ)

A: Differentiation of the function helps to find the derivative of the function. Simplification of the…

Q: 1. Find y' of tan(x²y*) = 3x + y² Answer: y': 3-2xy* sec²(x²y*) 4x² y3 sec2 (x2y4)-2y

A: We will solve the problem

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: DON'T USE CHATGPT Solve the following equation by canceling operator y"+y = 3x sin(x) (In the answer…

A: First of all we find the auxiliary equation for the corresponding homogenous equation. Find the…

Q: d/dx (2x'y²+8x-2y+3)=? Select one: a. xºy2 b. 14x°y? O c. 14x®y²+8 С. d. 14x°y²+2y O e. 2x'y?+8x-2y

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Q: d du 1) (sin-1u] dx %3D 1-u2 dx -1 du 리는 [cos-1 ul = dx V1-u2 dx d 1 du 3) = [tan-1 u] dx %3D 1+u2…

A: I have solved first three part for other repost question

Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: Find y' if y = 5x sin x. O A. y' = - 10 cos x+ 5x sin x B. y" = 10 cos x- 5x sin x C. y' = - 5x sin…

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Q: X₁. (x₁, Yr) (x', y') 0 (x, y) X x' = x + (x-x, )cos-(y-y,)sin y' = y, + (x-x) sin 0+(y-y,) cos P' =…

A: Solution:

Q: S -1 sin y³ +1 2 dydx

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Q: ignments: Find a solution for the following equations in two different ways: analytically and…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: i. y" - 4y + 5y = 39xe* sin(x) + 47e * sin(x)

A: