Let f (x,y, z) = xyz2 + 1 and suppose that x(t) = 2 – t, y(t) = In(t), and z(t) = 3t. df Use the multivariable chain rule (and correct notation) to find dt

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

A: The given equation is . Also .

Q: Use the Chain Rule to find dz/ dt or dw/ dt. z = xy3 - x2y, x= t2 + 1, y= t2 -1

A: Consider the given function z=xy3-x2y, x=t2+1,   y=t2-1 the chain rule, dzdt=∂z∂xdxdt+∂z∂ydydtwe…

Q: dz Use the Chain Rule to find dt for z = x2 + y2 + xy,x = sin t , y = e'.

A: z=x2+y2+xy ; x=sint , y=et

Q: (a) If w = e"yz, where x = and compute dw/dt when t = 0. (b) If f(x, y, z) function of s and t and…

A:

Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

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…

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:

Q: 10. Let w = f(x, y, z) = xe. If x = t², y = 1-t₁ z = 1 + 2t, use the partial dw dt derivatives and…

A: Using the chain rule and rule of partial derivative and get the required derivative.Final solution…

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:

Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

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 Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

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: Use the appropriate multivariable chain rule to find the indicated derivative. a. Let w = f(x,y,z) =…

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

Q: use the chain rule to find dz/dt, where z=x sin y, x=t^5, and y=5t^2 please show steps

A:

Q: Use the Chain Rule to find dz/dt. dz dt || z = √√√ 1 + x² + y², x = 2 In(t), y = cos(t) 1 √1+ (Int)²…

A:

Q: Let z(x, y) t° & y = 1+ 6t. = xe9 where x = dy and using the chain rule. dt dx dz by first finding…

A:

Q: 1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t…

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: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: Let y(t) satisfies dy dt 3ty-t-t 1+t2 for t2 0, and y(t = 0) = 1. Show that y(t) S 1+t for t2 0.

A:

Q: 1. a) Consider the function z = t², in which t = x – y. Use chain rule to compute dz the partial…

A: "Since you have asked multiple question, as per our guidelines we will solve the first question for…

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: dz Use an appropriate form of the chain rule to find dt z = 4x°y³; x = tº, y = t" Enter the answer…

A: From the given problem: z=4x6y3 ; x=t8 , y=t7 Now apply the chain rule.…

Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

A:

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 multivariable chain rule to find du/dt at t = 1, where w = sin(r²y), 1 = Int, y = 3t + 1.

A: To Determine: use the multivariable chain rule to find dwdt at t= 1 Given: we have w=sinx2y…

Q: Use an appropriate form of the chain rule to find dz/dt 1. 2 3xy; a r-t' and y

A: use partial derivative for finding drivative.

Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: Let f(x, y,z) = x² sin y + y e², where x = t + 3,y = net-1 and z = ln 2t. %3D df at t = 1 is: dt…

A:

Q: a)Let z = x?y – y² where x = t2 and y = 2t . Find dz/dt at t=1 using chain rule.

A: Given query is to find derivative is nge 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 x'+y' +z-9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x,y,z) (2,2,1)

A:

Q: Use the Chain Rule to find dz/dt. z = x2 + y2 + xy,    x = sin(t),    y = 3et

A:

Q: given that, x(t) =t2 +2    ,y(t)=t3 -2t  and f(x,y) =x2 sin(xy) . using the chain rule for partial…

A:

Q: Use the Chain Rule to find dz/dt. z = xy9 − x2y,    x = t2 + 1,    y = t2 − 1

A:

Q: Using the Chain Rule, find dz/dt for z In(x? + y²) and x = t, y = t²

A:

Q: If z = f(x,y) = tan x =t cose and y =t sin@. Use the Chain Rule method to find y as functions of t…

A: Given that z=f(x,y)=tan-1xy Where x=tcosθ,y=tsinθ Substituting, the values,…

Q: Using the second fundamental theorem of calculus and chain rule, compute t dt. t+1 dx 2x

A:

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: given z= f(x,y), where x = g(s,t) and y = h(s,t). chain rule for dz/dt is

A:

Q: Use the Chain Rule to find dw/dt. w = In V x2 + y2 + z2 x = 9 sin(t), y = 3 cos(t), z = 5 tan(t) dw…

A:

Q: dw Use chain rule to find dt if w = xez, x = t², y = 1- t, z = 1+ 2t.

A: Given w=xeyz, x=t2, y=1−t and z=1+2t We have to find dwdt by using chain rule. Hence, by chain rule…

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…

Q: Find dz/dt, for z= xy by using the Chain Rule.

A: Given function is  z=xy Let f(x,y)=xy Then z=f(x,y) Differentiate f partially with respect to x and…

Q: If z = e2x+ 3y and x = In t, y = t2, calculate dz from the total dt derivative formula and show that…

A:

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…