Suppose z = x² sin y, x = 3s² +lt², y= 2st. A. Use the chain rule to find and as functions of x, y, s and t. B. Find the numerical values of and when (s, t) = (3, 1). as at

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: Use this result and the chain rule to find (Isinx|) pr all x € (-T, T),x + 0. dx

A: Given,           ddxsinxWe know that,             The derivative of absolute function is given by…

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…

A:

Q: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

A:

Q: dw Use an appropriate form of the chain rule to find dt w = In(10x² – 4y + 5z³); c = t', y = tỉ, z =…

A: From the given function: w=ln10x2-4y+5z3 ; x=t12 ; y=t23 ; z=t-2 As we know that: The Power law:…

Q: B: Expressand as functions of u and v both by using the Chain Rule and by expressing z directly in…

A:

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

A:

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

A:

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

A:

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

A:

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

A: Express dw/dt as a function of t by using the Chain Rule. Use the sum rule and split the bracket.…

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: Find ?w/?s and ?w/?t (a) by using the appropriate Chain Rule and (b) by converting w to a function…

A: w=x2+y2+z2, x=tsins, y=tcoss, z=st2 a).…

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

A:

Q: Use the Chain Rule to find az/as and az/at. sin(0) cos(p), 0 = st7, p = s³t əz t³cos(p) cos(0) —…

A:

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: By using the multivariable chain rule, compute each of the following derivatives. (b) af/ds and…

A: (b) Given function is fx,y=exy Where, x and y is the function of s and t and defined as x,y=s-t,2st…

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

A:

Q: 1. Use the Chain Rule to find u and ou for w = x²y3 where x = dw at s2 +t2 and y = ds

A:

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: 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: (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 ôz/as and az/ðt. z = x°y5, x = s cos t, y = s sin t az as az at

A:

Q: Use the chain rule. If W=u^3 and U=t-1/t+1, find dw/dt when t=1

A:

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: w=x2+y2+z2,  x=cost,  y=sint,  z=et a).…

Q: 2. Use the Chain Rule to find for z = e¤/y where x = st and y = s2 +t

A:

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…

A:

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…

A:

Q: Suppose z = x´ sin y, x = 2s2 + 3t2, y = 6st. A. Use the chain rule to find z and as functions of x,…

A:

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

A:

Q: dz a²z and 1 a) Find- Usin chain rule. If z = e*y – Sin xy, x=-, y=t? дх ду dt

A:

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

A: Given : z=x2sin y x=2s2+3t2y=4st To evaluate: ∂z∂t,∂z∂s

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

A:

Q: Consider the following. w = xy2 + x2z + yz², x = t², y = 5t, z = 5 (a) Find dw/dt using the…

A: Details calculation is given below

Q: Suppose w = 2x2 + 8y², Compute dw/dt in two different ways: x = 7 cos(t) + 5 sin(t) , and y = 7…

A: The chain rule is mentioned below: dwdt=∂w∂x·dxdt+∂w∂y·dydt

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: Consider the following. w = xyz, x = s + 5t, y = s – 5t, z = st? (a) Find aw/as and ôw/at by using…

A:

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

A:

Q: dz dz and dv Use an appropriate form of the chain rule to find du 1 = Z = e&z*y; x = vuv, Y =-

A:

Q: 2 Let z=x ·sin(y) 2 X=S •t y= st. dz Compute & in two ways: (i) Using the chain rule and S ô t (ii)…

A: Given that , z=x2siny where x=s2t , y=st find ∂z∂s , ∂z∂t

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

A: Chain rule

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…

A:

Q: Suppose z = x² sin y, x = -s² – 21² , y = 8st. dz A. Use the chain rule to find and * as functions…

A:

Q: Suppose that f (x, y) is a function of two variables and that x(t), y(t) are functions of one…

A:

Q: Let z = f(x, y) and suppose x = 2u – 3v and y = 5u + 6v. Use the chain rule to express dz in terms…

A: x=2u-3vy=5u+6v Now we apply the chain rule  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u Take derivative of x  and y…