Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before differentiating. w = xy cos z, x = t, y = t2, z = arccos t

Q: Let z = x3 y2 ,x=t3, y=t+3 Use the chain rule to find dz at t=3 dt

A: By chain rule of partial derivatives,     dzdt=∂z∂xdxdt+∂z∂ydydt Here we have,       z=x3y2,   x=t3…

Q: Use an appropriate form of the chain rule to find dz/de 1. z = 3x?y; a =t and y = t? 2. z = 3 cos a…

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Q: Find dw/dt using the appropriate Chain Rule. Evaluate dw/dt at the given value of t.

A: The given equation is . Also .

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: dw Use an appropriate form of the chain rule to find dt w = 4 cos xy – sin xz; x y = t, z = t8 t'…

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Q: dz at (и, v) — (1,1) if du Use chain rule to find || a(w² - z + 1)-), : x = 3u – v, y = u°. 2 = x…

A: According to chain rule of differentiation . According to power rule of differentiation .

Q: Consider the following. w = cos(x - y), x = t2, y 52 (a) Find dw/dt by using the appropriate Chain…

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 6 cos xy – sin xz; x = t' y = t, z =…

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Q: Consider the function T = xe3x+y? dy 5 and dt where x = Vt + 1, and when t O we have y -2. dT when…

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 9 cos xy – sin xz; x = y = t, z = t3…

A: We have to find

Q: az and dz Use the chain rule to find as at sin(0) r = st, 0 = s9 + t° %3D as az at

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Q: Use the Chain Rule to find dw/dt. + y2 + z2 x = 5 sin(t), y = 7 cos(t), z = 6 tan(t) W = In

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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: Q1) Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

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Q: Consider the following. w = cos(x − y),    x = t2,    y = 21 (a) Find dw/dt by using the…

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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: tan(): '(), Suppose z = x = u cos(5v) , and y = u sin(5v) . Compute dz/du and az/dv in two different…

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Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: Consider the following equation: w=x2+y2 Substitute x=cost+sint and y=cost-sint in the above…

Q: Find aw/at using the appropriate Chain Rule. w = x sin y x = e', y = - t dw dt

A: Derivative

Q: Suppose z = x² sin y, x = 2s2 + 3t2, y = 4st. dz and A. Use the chain rule to find ds as functions…

A: Given: z=x2siny x=2s2+3t2 y=4st To find: Using chain rule, ∂z∂s and ∂z∂t ∂z∂s1,-2 and ∂z∂t1,-2

Q: Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3 , by using the Chain Rule dt

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Q: d use the Chain Rule to calculate f(r(t)). dt f(x, y) = x² – 3xy, r(t)= (cos t, sin t), 1 = }

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Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: Use the chain rule to find if y = 2wz + z², w = e*, z = cos x

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

A: As indicated in the question, we will make use of chain rule of differentiation. Recall that the…

Q: Given that w= x² +y³ +tª, x= siny and y =e'. Which of the following is a correct chain rule for…

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Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: w=x2+y2, x=cost, y=sint, t=π, We have to a) express dWdt as a function of t, both by using the Chain…

Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A: We find dw/dt using chain rule. Here plug x = cos t, y = sin t, z = 4sqrt(t) and simplify.

Q: Use the Chain Rule to find dw/dt. w = In(V? + ° + z2 x = 3 sin(t), y = 2 cos(t), z = 5 tan(t) dw dt

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Q: Use the Chain Rule to find ôz/as and az/ðt. z = x°y5, x = s cos t, y = s sin t az as az at

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Q: Consider the following. w = cos(x - y), x = t2, y = 1 (a) Find dw/dt by using the appropriate Chain…

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin cz; x = y=t, z = t7 t'…

A: Here we have to find dw/dt by chain rule.

Q: If = Z sin x = 2t, y = 2 – t2, find dz/dt using the chain rule. Assume the variables are restricted…

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Q: IF V = xsin(y) + ye where x = s + 2t and Y = st Use the chain rule to find dv and- ds dt when s=0…

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Q: Consider the following. w = cos(x - y), x - t2, y = 59 (a) Find dw/dt by using the appropriate Chain…

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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: Let T = x²y - xys + 6x, where x = r cos 0 and y = r sin 6. Use the chain rule to find dT/00.

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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: dy If y = tan t , x = tan? t ,Find by using Chain Rule dx at t =

A: Let the two functions are xt and yt. The chain rule to find dydx is given by the following formula.…

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 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: (a) express dw/ dt as a function of 1, both by using the Chain Rule and by expressing w in terms of…

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Q: Consider the following. w = xy cos z, x = t₁ y=t5, z = arccos t (a) Find dw/dt by using the…

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Q: Let w f(t,0) where t and 0 are functions ofr and s, %3D dw is equal to Or then according to the…

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Q: Use the Chain Rule to find dz/dt. z = sin(x) cos(y),    x = The Square Root of t,    y = 8/t

A: Given: z = sin(x) cos(y),    x = √t,    y = 8/t By Chain Rule,

Q: Find dy/dx if y = x by using the Chain Rule with y as a compositionof y = 1 + (1/u) and u = 1/(x -…

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Q: Use the chain rule to find ∂w/∂t given w =√ x^2 + y^2 + z^2 and x = cos(st), y = −2s ln(t) and z = s…

A: Solution:Given      w=x2+y2+z2x = cos(st), y = −2s ln(t) and z = s − 3t.To find…