dw 13. Express as a function of t in two ways: (a) Using the Chain rule, and (b) First express w as a function dt dw of t and directly differentiate with respect to t. Evaluate at the given value of t. dt (13a) * w = x2 + y?, x = cost + sin t, y = cost – sin t, t=0 (13b) w = z – sin(xy), x = t, y = ln t, z = et-1, t=1

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

A: Given- w=x2+y2, x=cost, y=sint and t=π To Find- The value of dwdt as a function of t, both by using…

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: tan (X) where : Let z=f(x,y) = (10 + 23x)y" where : 13 - e (t – 1) + tan'(t) , and y= (2- t) e'-…

A: Here, the given functions are: z=f(x,y)=(10+23x)ytan xx=13-e2e(t-1)+tan-1(t)y=(2-t)et-13(t-1)

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: Use the appropriate form of the chain rule to find the derivatives. w = 11x² + 11y² + z²; x = p sin…

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Q: dw For the functions w = - 2x + y, x= cos t, and y = sint, express as a function of t, both by using…

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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…

A: We have to find

Q: Consider the functions z= - e In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as…

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

A: we have to find the following derivatives using chain rule

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

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Q: dw Use the Chain Rule to find where w = cos 12x sin 4y, x = - dt and y = t". 4 dw

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Q: (型) y = 4 – t, z = cos x = 3t, find dz/dt using the chain rule. Assume the variables are restricted…

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Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x sin y x = e', y = n - t t = 0 dw…

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Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x sin y x = e', y = n - t t = 0…

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

A: Given, 1. w = x2 + y2 , x = cos t,  y = sin t;  t = π  2. w = x2 + y2 , x = cos t + sin t,  y = cost…

Q: dw where w sin 8x cos 3y, x= dt Use the Chain Rule to find 2 and y = t". dw dt (Type an expression…

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

A: A) The function x is differentiated as, x=cost⇒dxdt=-sint The function y is differentiated as,…

Q: Find the rate of change of w with respect to / at t = 1 by using the chain rule. You can check your…

A: Given w=x7y3z3     ;    x=t6    , y=t+2    ,   z=3t4

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: 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: 2n dw at t= dt dw For the functions w = 3x - y, x cos t, and y = sin t, express as a function of t,…

A: Given,

Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; x = ;, 1 y = 9t Enter…

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Q: Q3/ For below (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w…

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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: The equation implicitly defines z as a function of t. Find dz dt 11 dt cos (3 z) = -8

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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: (a) Consider the provided equations, w=2yex-lnz, x=lnt2+1,y=tan-1t  and z=et ; t=1  Express dwdtas a…

Q: dw at t= dt For the functions w = - 4x + 10y, x= cos t, and y = sin t, express as a function of t,…

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

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Q: Consider the functions z = - 5 e* In y, x = In (u cos v), and y = u sin v. dz and dv (a) Express as…

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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: 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: 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: 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: 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 For the given functions, (a) express dw dt as a function of t, both by using the chain rule and…

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Q: Consider the functions z= - ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as…

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

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Q: dw Q1: Evaluate dt at given value of t by using the chain rule 1- w = x2 + y² x = cos t + sin t 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 function g(x, y) = tan¬(1 – x) + 3e2"-y and the point P (1, 2). %3D a. Use the…

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Q: 28. Suppose you follow the spiral path C: x = cos t, y= sin t, and z= t, for t20, through the domain…

A: NOTE: You have posted a question with multiple subpart, we have given answers to the first three…

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: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Consider the following. w = cos(x – y), x = t2, y = 9 (a) Find dw/dt by using the appropriate Chain…

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Q: бх? + 4y, : Suppose w = Compute dwldt in two different ways: x = 5 cos(t) +7 sin(t), and y = 5…

A: NOTE-By bartleby rules, only first three question has been answered. As per given by the question,…

Q: Q2) Use the chain Rule to find dw\dt of y w = =+2,x = cos²(t), y = sin² (t), z =, at t = 3

A: In this question,w is function of x,y,z and x,y,z are the function of t so first we find out…

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

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Q: Q2/ Express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.