Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

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

A: These questions are about ordinary differential equation.

Q: 10. sec (10t) tan" (10t) dt 11. tan" (2w) sec" (2w) dw / cot (3r) csc® (32) dæ 12.

A: As per our guidelines, I can answer maximum one question. Since you have asked for three, So i did…

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: x³y' +3x?y" +xy' +8y=xInx Select one: a. YG.S +x(c2sin3lnx+c3cos3Inx)+x ( Inx -) - Inx: b.…

A: Given equation is  x3y'''+3x2y''+xy'+8y=xlnx            (i) Let x=et. Then…

Q: Hiw/ Find F'(x) 1. if F(x) = x, tanx 2-if y = Sinx it casx 3- Find g" ()if y co) = Sec y ex) g ex)…

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Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

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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: Find nd cos(z ² + y²)dA where D = {(x, y) | 16 ≤ x² + y² ≤ 81} D

A:

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: (ysin x+xy cos x)dx+(xsin x+1)dy = 0 Ans. xy sin x+ y = c

A:

Q: Hiw/ Find F'(x) 1 x, tanx if F(x) = X 2-if y= Sinx 3-Find y" (I)if yex) = Sec

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Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: tan x= Sin 2X

A: Given: y'+y tan x= sin2x

Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

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: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

A:

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: Q2) Find the general solution for this equatio- y" + (tanx-2cotx)y' + (2cot²x)y = 0 If you know that…

A: Given differential equation It has one solution Lets use method of reduction of order.Assume the…

Q: L (sin? t) What is f (t), f' (t) and f (0) ? O b) O a) f (t) = sin t, f' (t) = 2 cost, f (0) = 0 f…

A: We will find out the required solution.

Q: y= (12,4 + x)* + (1+)(Va² +x- c )cos²(4x), c)cos²(Ax), 3)4( 3 y = (12,4 +x)* + (1+x' Зx +x — с y = ?

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

A:

Q: 2. y" +4y= sin2x + x2 using inverse operator method

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Q: In implicit differentation problems it seems we treat x and y differently. For example, when we…

A: Recall: Chain Rule of differentiation :    If F(x)=f(g(x)) then ,   F'(x) = df(g(x))dx =…