Tutorial Exercise Find dw/ds and dw/at by using the appropriate Chain Rule. w = x cos yz, x = s², y = t², z = s - 7t Step 1 dw by using the Chain Rule on each term. ds Find dw as dw ax dw dy , dw dz dx as dy as dz as = cos(yz)(s?) - ( xz sin (yz) 1: sin(y:))) – xy sin(yz) s- 7t ds s - 7t Step 2 Substitute the values of x, y, and z and find the partials with respect to s. aw cos(yz)(s?) – xz sin(yz)(?) – xy sin(yz)(s – 7t) - XZ ds ds as II

Q: Find dw/dt using the appropriate Chain Rule. Function w = x sin y x = e", y = 1 - t Value t = 0 X =…

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Q: dz Use an appropriate form of the chain rule to find dt - = 2a°y°; x = t°, y = t5 Enter the answer…

A: Topic = Derivative

Q: dz Use an appropriate form of the chain rule to find dt = 2.0°y³; x = t°, y = t5 = Z Enter the…

A: Here, the given functions are: z=2x9y5,x=t8,y=t5 So, z is a function of x and y and x and y are…

Q: Current Attempt in Progress dz Use an appropriate form of the chain rule to find dt 1 y = 7t z = 9…

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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: Q) Use the chain rule to express dy / dx in terms of x and y for the :following y =1-! 1 t = 1-x and…

A: Consider: y=1-1t and t=11-x. Calculate dydxin terms of x,y at x=2. Calculate dydt and dtdx using…

Q: dz 922 – 4y², x = 2 sec t, y = 3 tan t. Using the chain rule, find dt Given z =

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Q: dx Q2 / Use the chain rule to find ( ) in terms of x and y dy y = ( 2 1 1, at t2 t = 2 and X t + 1.

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

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Q: dz appropriate form of the chain rule to find dt Use an = 6x³y³; x = t", y = t10

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Q: dz Use the Chain Rule to find where z = 4x sin y, x=t*, and y = 4t°. dt' dz dx II

A: Given z=4xsiny, x=t4 and y=4t5 We have to find that dzdt Chain rule is defined as f⋅g'=f'⋅g+f⋅g'…

Q: dz Use the Chain Rule to find where z =x cos y, x =t°, and y = dt dz dt

A: We have to find the derivative using chain rule, so,

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 4 cos ry – sin cz; x=÷, y = t, z= t8…

A: Given,           w = 4 cos zy - sinxz;            x = 1/t ,      y=t,        z= t⁸

Q: dw Use an appropriate form of the chain rule to find dt w = 4 cos xy – sin xz; 1 x = ; y = t, z = t8…

A: A detailed solution is given below

Q: 2s – 5t & y = 6s – 8t. %3D Let z(x, y) = x + 9y? where x = az дх ду да dy dz Calculate ds & and…

A: We use the chain rule

Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

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Q: dz 3 Use the Chain Rule to find where z= 2x sin y, x=t°, and y = 3t°. dt '

A: Given,           z=2xsiny , x=t5 and y=3t3.

Q: Use the Chain Rule to find dz where z = 2x cos y, x=t, and y = 5t. dt dz dt (Type an expression…

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Q: Use the Chain Rule to find dz/dt. z - x2 + y2 + xy, x = sin(t), y - 2e Use the Chain Rule to find…

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Q: Compute dy/dx using the chain rule in formula. State your answer in terms of x only.  y = u3>2, u…

A: Given equations - y = u3+2           .....(1)                                                  In…

Q: dw given w = a2 + 2y2 + 22 and a = cos (st), y = -2s Int and Use chain rule to find 2 = 3s' Vi.

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Q: ら)1f u-L -*9 sin (2x ty), x = s? + 2t" and y= 2s -t" au using at find the chain rule Ond as

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Q: as and dw/t using the appropriate Chain Function Values W = sin(4x + 5y) X = s + t, y = s – t %3D TC…

A: Given  w=sin4x+5y   x=s+t       y=s-t

Q: dz Use an appropriate form of the chain rule to find dt z = 3x"y"; x = t, y = t5 Enter the answer in…

A: Given that , z=3x7y7 ;   x=t5 , y=t5 dzdt=?

Q: = xy³ + x2y, x = 31- 8, y = 4t2 - 4. dw when t 1. dt Use the Chain Rule to calculate dw dt

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Q: dz Use an appropriate form of the chain rule to find dt z = 5x*y°; x = t1º, y = t" Enter the answer…

A: NOTE: Refresh your page if you can't see any equations. . take partial derivative with respect to x

Q: dz at (s, t) = (0, 1) if Use chain rule to find ds "(). = e0* – st, y = s² – t2. z = 6x + y² tan x =…

A: We know that the  chain rule is the formula in derivative to compute the derivative of a composite…

Q: dv dv 5. Use the Chain Rule to find and ds v = ln (2.x + 3y), where x = s sin t, y =t cos s %3D

A: Here, Givenv=ln(2x+3y)∂v∂x=22x+3y∂v∂y=32x+3yAlso, x=s sin(t)∂x∂s=sin(t)∂x∂t=s cos(t)y=t…

Q: Use the appropriate form of the chain rule to find the derivatives. w = 3x? + 3y² + z²; x = p sin ø…

A: Given:   w = 3x2 + 3y2 +z2  x and y and z values is given

Q: dz dz Use an appropriate form of the chain rule to find and du dv' = e2x²y; 1 Vuv, y= z x = Enter…

A: Explanation of the answer is as follows

Q: the Chain Rule to find dz/dt. z = cos(x + 7y), x = 5t5, y = 3/t dz %3D dt -sin 5 + 21 254 21 II

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Q: dx Use the chain rule to find () in terms of x and y dy 2 y = ( and X = t2 at t= 2

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Q: Find dw/dt using the appropriate Chain Rule. Function Value t = 0 w = x sin y x = et, y = n - t dw…

A: Given query is to find the indicated derivative.

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = y = t, z = t³ t…

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Q: use an appropriate form of the chain rule to find dw/dt. w=6cosxy-sinxz; x=1/t, y=t, z=t^8. enter…

A: Given: w=6cosxy-sinxz x=1t, y=t, z=t8

Q: x²y + 3xy* where x = sin 2t and y = cos t. Use the chain rule to dz find 3. Let z when t = 0. dt

A: To use the chain rule to find dz/dt at t=0

Q: dz dz (a) Write down the formula for and when z f (x, y), x = x(s, t) and = y(s, t). ds dz (b) Use…

A: The detailed solution is given in the attached Handwritten notes.

Q: dz Use the Chain Rule to find : z = = cos(x + 4y),x = 5t*, y = - %3D dt

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Q: Use the chain rule to find dz/t. z = x² + y² + xy, x = sint, y = et

A: Here we will find dz/dt,

Q: dz (b) Determine the by using the Chain rule with the following information: ds 2 X = - s2 2 7 z =…

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Q: dw Find using the appropriate Chain Rule for w = cos(4x−4y), where x = tº and y = 3. dt

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Q: dw Evaluate at the given value of t, by using the Chain Rule, dt w = 2ye* - Inz, x = ln(t² + 1), y =…

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Q: dz where z=x sin y, x=t°, and .3 se the Chain Rule to find dt ype an expression using t as the…

A: Solution of the problem as follows

Q: dz Use chain rule to find at (s, t) = (0, 1) if ds z = 6x + y² tan e – st, y = s² – ť. x = ebs

A: Consider a function of multivariable where and . Then according to the chain rule for…

Q: dz dz and du Use an appropriate form of the chain rule to find dv' z = =; x = 14 cos u, y = 5 sin v…

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Q: Find dw/dt using the appropriate Chain Rule, Function Value w = x sin y x = e°, y = x –t t = 0 dw dt…

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Q: dz dz and ds' at C) Use the chain rule to compute for dsðt z = x²y, x = sin(st), y = t2 + s². dw dw…

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Q: x²y + 3xy where x = sin 2t and y = cos t. Use the chain rule to dz when t = 0. 3. Let z = find dt

A: According to our guidelines we can answer only first question.

Q: Q NO: 04 find d, dx (a) Let y (b) Let y = (-1) , find Y using chain rule dx

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Q: dw 3. Given w=ln (x²+y) where x=2t , and y=4-t . Find in two ways: dt (a) Using the appropriate…

A: Given:- w = ln(x ^ 2 + y) where x = 2t , and y = 4 - t . To find:- dw/dt (a) Using the appropriate…