Consider the following. w = xyz, x = s + 5t, y = s – 5t, z = st? (a) Find aw/as and ôw/at by using the appropriate Chain Rule. aw as at (b) Find ôw/@s and ow/at by converting w to a function of s and t before differentiating. as at

Q: Consider the following. w = x - ¹₁ x = e³t, y = t³ (a) Find dw/dt by using the appropriate Chain…

A:

Q: az and as az 4. Using Chain Rule, determine for the following functions at (a) z = x'y where x =…

A:

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: 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: Please help

A: Let,

Q: az az Use the chain rule to find and as at Z = In(3x + 5y), x = s sin(t), y = t cos(s) az az at

A:

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

A:

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

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

A:

Q: 5.) Suppose z = f (x, y) , where x=x(t,r) and y= y(t,r). Assuming all the functions involved have…

A:

Q: 14.11 Let f(x, y) = 3xy² + 2x where x(t) -312 and y(t) = 4t3 + t. %3| || %3| a) Use the Chain Rule…

A:

Q: Consider the following. ху W = x = 3r + t, y = rt, z = 3r – t aw aw and ar (a) Find by using the…

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: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

Q: Suppose z = x2 sin y, x = 2s? + 3t2, y = 6st. A. Use the chain rule to find and as functions of x,…

A: (A) ∂z∂s=∂z∂x.∂x∂s. Take derivative of z=x2siny w.r.t x : ∂z∂x=2xsiny=4s2+6t2sin6st. And, ∂x∂s=4s.…

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

A: Solve for partial differential

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 ?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: Let f (x, y) = 3x – 2²y. x = -t, y = s + 2t dz dz Use an appropriate chain rule (involving , , etc.)…

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: Suppose T = f(x, y) = 50+y. Write down the chain rule in the appropriate variables and use it to…

A: Given: T=fx,y=50+xyx=xt=2costy=yt=sint

Q: Consider the following. w = X - x = e2t. y = t3 (a) Find dw/dt by using the appropriate Chain Rule.…

A:

Q: a) by using the chain rule and (b) by converting w to a function of t before differentiating w=…

A:

Q: If the 2n RVs A, and B, are uncorrelated with zero mean and E(A²,) = E(B²,) = %3D o, show that the…

A:

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: xy ) Suppose thot fixy)=e , x(4,0)= 3uSiina, glu, vl = f(x (4,v), yluiv), find , by using Chain Rule

A: Using the chain rule,

Q: Let z = tan-1(E) – In(cos y), where r = T- u and y = uv. Use multivariate chain rule to find the…

A:

Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

Q: Suppose z = x² sin y, x = 3s² +lt², y= 2st. A. Use the chain rule to find and as functions of x, y,…

A: Consider:z=x2sin y, x=3s2+t2, y=2st. A1) Find ∂z∂s. Apply chain rule ∂z∂s=∂z∂x·∂x∂s+ ∂z∂y·∂y∂s Find…

Q: az and as az Use the chain rule to find at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az at

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: (a) Consider the provided equations, w=2yex-lnz, x=lnt2+1,y=tan-1t  and z=et ; t=1  Express dwdtas 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: 2. Use the Chain Rule to find for z = e¤/y where x = st and y = s2 +t

A:

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

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: Consider the following. w - xy + xz + yz?, x= t, y- 7t, z-7 (a) Find dw/dt using the appropriate…

A: We have to use chain rule to solve the question.

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: Consider the following. w = In(x2 + y), x = 2t, y = 8 - t dw by using the appropriate Chain Rule. dt…

A: Solution is given below..

Q: Consider the following. w = ln(x2 + y),    x = 2t,    y = 4 − t (a) Find  dw dt by using the…

A:

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

A:

Q: Consider the following w-xyz, x s 4t. y-s-4t, z- st (a) Find dw/ds and dw/dt by using the…

A: If F=f(x,y) and  x=g(t) and y=h(t),then     ∂F∂t=∂F∂x∂x∂t+∂F∂y∂y∂t

Q: Suppose w=x/y+y/z, where x=e^(4t), y=2+sin⁡(4t), and z=2+cos⁡(3t). A ) Use the chain rule to find…

A:

Q: Q1) Suppose w =÷+ ?, x = cos² t, y = sin² t, z = ; Evaluate dw at t = 3, by using the Chain Rule dt

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…