dw Use the Chain Rule to find , where w = sin 8x cos 2y, x= and y =t. dt dw dx (Type an expression using x and y as the variables.)

Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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

A: Substitution is done.

Q: Use this equation to find  dy/dx. 5y cos(x) = x2 + y2

A: Given:

Q: Find dy/dx and d2y/dx2. x = 8? + cos ?,    y = 9? − sin ?

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Q: dw Use the Chain Rule to find where w= cos 12x sin 4y, x=5, and y =t". dt dw dt (Type an expression…

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Q: dz Find in the function ryz + a’yz = cos (xyz) CoS az

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Q: d²y Find 2 dx? y = sin 2x+cos² x

A: Using derivatives.

Q: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: Given that y = sin (t) and x cos²(4t*), hence find dx dy

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Q: Find dz/dx if z is implicitly given by the equation ze-y = sin(ryz).

A: Given, zex-y=sinxyz It is simplified as follows: Differentiate both sides with respect to x and…

Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: dw H.W: Use the chain rule to find the derivative dt with x = cos x = cos² t, y = sin² == and…

A: Given :w=xz+yzx=cos2t    and y=sin2t   z=1t

Q: dw of w -+ dt X y H.W: Use the chain rule to find the derivative dw with x= cos 1, y = sin? t, z =-…

A: We differentiate the function with respect to t.

Q: du = 3 and dx dy = cos u, find the du dy Given y = sin(3x – 2). If dx 3 cos(2x) 3 cos(3x) 3 cos(3x –…

A: Topic:- derivatives

Q: dy Let y=e* sin 3x. Show that 3e-2* cos 3x - 2y. dx -2x d'y = -13y-4- dr Hence show that dx

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Q: Q3.a) Find if y + SE rsecx -dt = xy sint+1 dz Q4.a) if z = sin²0, and 0 = w² + cos (w) find-

A: 3a):  y+∫xsecx11+sintdt=xydifferentiate both sides and use Leibniz rule for differentiating the…

Q: Find DE using variable separable cos/dx + 1/ydy=0

A: Given that: cosxdx+1ydy=0

Q: 4. Find d2y/dx? for the following functions: a) y = sin x2 cos 2x b) y = cos (sec? 3x)

A: Given that  a)y=sinx2cos2x b)y=cos4sec23x find d2ydx2

Q: dy Find dx 1. (a) y= cos (sinx)

A: topic - derivative of a function

Q: 5-2x dy if y = cos Find dx %3D 5+ 2x

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Q: dy Find dx for y = 14x +5 coS x. d(14x+5 cos x)%3D

A: Formulas:1. ddxxn = nxn-12. ddxcosx = -sinx

Q: dz and du dz Use an appropriate form of the chain rule to find dv ; x = 16 cos u, y = 3 sin v Enter…

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Q: Let y = tan(3x + 7). Find the differential dy when a = 4 and dæ = 0.3 Find the differential dy when…

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Q: Calculate L{e-# cos(2t – r)}

A: We have to calculate : Le-2tcos(2t-π) First we will calculate , Lcos(2t-π)…

Q: Use this equation to find dy/dx. 4y cos(x) = x² + y2

A: We will differentiate  equation with respect to X.

Q: The integrating factor that can be used to turn the following non-exact equation into an exact…

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Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

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Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx) y = (tan x + sin…

A: The given function is y=tanx+sinx-3 We have to find dydx by using Leibniz’s notation for the chain…

Q: Let y = tan(2x + 2). Find the differential dy when x = 4 and dx = 0.2 Find the differential dy when…

A: We have to find change in y

Q: Find dy/dx of y=sin-!x+cos-4 dy/dx is Blank 1. Blank 1 Add your answer

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Q: d. t sin 2 dt COS dx 3

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Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: Q4: Find dy\dx if|cos'y +5y? = x?

A: The given equation iscos2y+5y2=x2to find dydx

Q: 2T -TT Evaluate: S. (sin x + cos y)dx dy II SII 71I

A: Let give integral is equal to I

Q: A ) Find ſ cos 5t dt B) If y = x² + , x = 2t -5 then find dt

A: A)-     I=∫Cos5t dtlet 5t=uderivating both sides5 dt = duSo,I=15∫Cos u du = 15 Sin u +C…

Q: 4. Find d²y/dx² for the following functions: a) y = sin x? cos 2x

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Q: -x2 + 5 2. y = cos 2x³

A: Given: y=-x2+5cos2x3

Q: dx dy Suppose x and y are functions of a third variable t. If sin²(x)+cos²(y) =- and dt 1, what is…

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Q: find dy /dx for the following 3 2 -1 Y3x'+Sin x+ Sin5X

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Q: Let y = tan(4r + 8). Find the differential dy when a = 4 and da = 0.3 Find the differential dy when…

A: Differential equation: - A differential equation is an equation that contains the derivative of an…

Q: Let y = =tan(4x + 6). Find the differential dy when x = 5 and da Find the differential dy when x = 5…

A: A detailed solution is given below.

Q: dt cos?(t) dr dx du du + ex- at cos²(t) :-7u, ex dr du -7u dr t(0) = 0, x(0) = a, u(0) = e et heR.

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Q: Consider the implicit function. ev = sin (2x) dy in terms of x. dx Determine the formula for dy dx

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Q: dx y of y = dy cos-1(ln (xy)) Find

A: We write cos-1 as acos for simplicity. The derivative is too complex. So, we take the help of an…

Q: Find dy dx 12) y = cos ³ (5x+2) -2)) y = √tan √√₂x + + 3)) Por The following Function i y = sin-¹…

A: **As per our guidelines, we are supposed to answer only 3 subparts of a question. Since you have…

Q: dw Find dx where w = cosz- cos 4x cos'4y + sin 4x sin 4y and z= 4x+ 4y. dw 口

A: lfirst put value of z and then expand cos term Now we get Zero whose derivative is zero

Q: dw of w==+ dt x. y Use the chain rule to find the derivative with x = cos 1, y = sin ?t, z = - dw…

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Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

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Q: What is general solution of the given ODE. * dy cos? (x – y+ 1) dx .2 COS

A: