au %3D ax at u(x, 0) = 0 ди (x, 0) = 0 at u(0, t) = sin? t u(1, г) — 0,

Q: y = (sin x)e¯* find de sin-1y %3D d In x

A: y=sinxe-x. Then we have to find desin-1ydlnx.

Q: y sin(Vu +3u-1) Oy = Vx x+ vZx y = e* sec(tan(x*)) y%3D u = In cos(x? + 1)|

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Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: S cos ædx from a = 0 to b = %3D %3D 3.

A: Substitution is done.

Q: (x – cos y)dx – sin ydy = 0 Of (x, y) = -xe-# +e-* cos y + k (y) ;f (r, y) = -e- sin y dy +k (y) Of…

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Q: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

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Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

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Q: Solve the homogeneous DE. 3. (x – y sec?2 – x tan2) dx + x sec² 2 dy = 0 -

A: Given that: x-ysec2yx-xtanyxdx+xsec2yxdy=0

Q: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

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Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: (e* + In y +) dr + + In a + sin y) dy = 0

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: (x+y²); x=e°cosu, y= e'sint at (u,v)= (/3,0). Let T= xy la (x+y²); sinu. ン

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Q: z= cos y Using the substitutions the DE (3cos y - 5x) dx – 2x?tan y dy=0 reduces to dz= - sin y dy

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Q: dw w=x +y, x-cos r, y-sin/ ise dt Irm

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Q: dy at the given point. dx Calculate sin² (–5y) = x + y, - %3D 4

A: Given equation sin2(-5y)=x+y and point 2-π4,π4 The objective is to calculatedydx at the point.

Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

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Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: d²y 1.) of y = sinInß and x = In(Inß) dx2

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

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Q: dw "(1),y = sin (1),-: 2) w=+ x= cos at =3 Ans. -1 dt

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Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sinh (xy - z2)

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Q: Siny dy = Cas y (l-x Cosy) Cauy) %3D

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Q: cos(t)y/" + sin(t)y/ + t³y = t² +1; y(0) = 2, y (0) = 3 COS

A: Our objective is to find the interval on which a unique solution exists.

Q: (cos y- zsee'y) de – sin y dy = 0

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Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: 22. u- Vr? + s, r- y + x cos 1, s -x+ y sin t; ди ди ди when x= 1, y = 2, 1 = 0 ar ay at

A: Given: u=r2+s2  r=y+x cos t and  s=x+y sin t By using Chain Rule we have to find: ∂u∂x, ∂u∂y ,and…

Q: O1 Find: fx³ cos x dx using Integration by parts b. ſ cosx? 2x dx using Substitution Method a.

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Q: 7. (a) Find dy/dx, when x = a(1 + cos 0), y = a (0 + sin 0). (b) Differentiate xcosx w. r. t.…

A: Differentiation using Logarithms: When a function appears as an exponent of another function we make…

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

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: 31. f(x, y) = e cos y a. (0, 0), b. (0, п/2) %3D at

A: We know that linearization of f(x,y) at (a,b) is

Q: The integrating factor of the equation sec? y + xtany= x° is: dy de In|sina| O None of these…

A: We have to find I.F

Q: 2- y" + 4y' + 20 y = 23 sin t - 15 cos t y(0) = 0 , y'(0) = -1 %3D

A: Differential equation is, y''+4y'+20y=23sint-15cost Given conditions is, y0=-1y'(0)=1

Q: dy/dx=(x+siny)/(2y-xcosy) is an exact equation

A: Given that dydx=x+sinyy-xcosy we need to check that it an exact equation

Q: b) Differentiate y = e (In3x) + tan (3y) with respect to x. %3D + 2e In 3x Ans: dy %3D 3 1-

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Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

Q: dW Find at t=0, if dt .3, W = x*y+ zxy whe x = sin2t, y = cos ?

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Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, y₂ ) is…

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Q: Let y=3sqrt(x) Find the change in y, Δy when x=2 and Δx=0.3 Find the differential dy when x=2 and…

A: We are going to solve

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

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Q: h of the DE's =)y = 2 sin² x ; y(0) = 0 , y'(0) =-2

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Q: Find dz/ðx , dz/ðy at the point (1,1,1) if x³ + z² + ye + xz cos y = 0

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Q: Exercise 5 Normal. , e-x² dx = \TT -00 Use 1? = (Se-x* dx)( S,e-y² dy) = L. Le-(x²+y²) dx dy = Sp2…

A: Find the valve of the integral

Q: Can you help me step by step?

A: Given information: