Use the Chain Rule to find dw where w = sin 8x cos 2y, x = , and y = t°. dt 2 dw dt (Type an expression using t as the variable.)

Q: c) dx E (sin cos) dt

A: We find ddx ∫xπ/2   sint2   cost3 dt

Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = " 2. II

A:

Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

A:

Q: dw Use the Chain Rule to find where w= cos 12x sin 4y, x=5, and y =t". dt dw dt (Type an expression…

A:

Q: Use the appropriate form of the chain rule to find the derivatives. w = 3x? + 3y2 + z²; x = psin o…

A:

Q: Q. Find F(s): e-Tt St cos? 3t dt.

A: Q. The given integration is,∫0tt cos23t dt

Q: A) Use the chain rule to find where w'sy',x= sint + cost y = cost - sint. B) If f(x. y) - xy?+ x'y ,…

A:

Q: r(t) = t cos ti + tj + t sin tk, t > 0

A: The graph is increasing linearly along the y-axis. So, yt=t   Looking at the graph from the y-axis,…

Q: Use the Chain Rule to find dz/ds and dz/ot In(3r + 2y), a = s sin t, y = t cos s.

A:

Q: Use the appropriate form of the chain rule to find the derivatives. 3x? + 3y2 + z2; x = p sin o cos…

A:

Q: Find the value of dy/dx at the point defined by the given value of t. x 5 sin t, y = 5 cos t, t= O…

A: Given, x =5sint  y =5cost We have to find the value of d2ydx2 at t = 3π4

Q: Use the Chain Rule to find dw/dt, where w = sin 8x cos 2y, x = t/2 , and y = t4 dw/dx (Type an…

A: Please see the explanation below

Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x – sin ry; y = 9t t %3D SSEVS Enter…

A:

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

A:

Q: Find the value of dw/dt if w = x2+y2, x = 26 cost and y = 26 sint

A:

Q: Given z = z?xy – tan(xy) where x = sin (5t + 2) and y = t3 + 4t. By chain rule, || dz find dt

A:

Q: If V = x² + y² where, x = a cos t, y= b sin t, find AP and verify the result. dt

A: x=acost y=bsint V=x2+y2 put the values of x and y V=acost2+bsint2 V=a2cos2t+b2sin2t

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

A: Chain rule

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: 5xy dx+ 2xy dy, where Cis the rectang

A:

Q: Find the general solution of du 2u + dt cos t t t

A:

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…

A:

Q: Use the appropriate form of the chain rule to find the derivatives. w = 3x? + 3y2 + z²; x = p sin o…

A:

Q: Find dy and evaluate when x = T and dx 0.5 for the function y -10 cos (5x)

A:

Q: z = cos(10xy) %3D dz %3D

A:

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

A:

Q: Use the Chain Rule to find dz / dt or dw/ dt.(odd) z=e^r cos(theta), r=st, theta=squart of (s^2+t^2)

A:

Q: Given a = 2 cos t + 3 and y = 3 sin? t dx dt dy %3D dt dy da

A: From the given problem:   x=2cost+3  &  y=3sin2t   So, a)…

Q: Find the general solution dy y cos a + 3xy %3D dx

A: We solve the given differential equation by separation of variables.

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: dz and du dz Use an appropriate form of the chain rule to find dv ; x = 16 cos u, y = 3 sin v Enter…

A:

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

A:

Q: The acceleration of a particle moving back and forth on a line is a = d2s/dt2 = pai ^2 cos pai t…

A: Given information:

Q: dz when du Use the Chain Rule to find = e' cos 0 and r = 3uv, 0 = Vu? + v². sin A

A:

Q: ,2 4 +(dx dt 2 dt ....

A:

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

A:

Q: a²z + ax? (c) Show that the function z = e* sin y + e cos x satisfies Laplace equation a²z = 0. ду?

A: Since you have posted multiple questions in this question which are not interlinked so I do first…

Q: Use the Chain Rule to find dw/dt. x = 6 sin(t), y = 2 cos(t), z = 9 tan(t)

A:

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…

A:

Q: cos(4x) dx - Find the Cauchy principle value (showing details): J (+5x2+4)

A: Given integral is, I=∫-∞∞cos4xdxx4+5x2+4 So, the function is, fz=cos4xdxx4+5x2+4 Now, consider the…

Q: dz where z=x sin y, x=t°, and .3 se the Chain Rule to find dt ype an expression using t as the…

A: Solution of the problem as follows

Q: Consider the following. w = y? - x, x= cos(t), y = sin(t) dw by using the appropriate Chain Rule. dt…

A: given: w=y2-x, x=cos(t) and y=sin(t) (a) we have to find the value of dwdt by using the appropriate…

Q: dz Use an appropriate form of the chain rule to find dt z = 3 cos sin ry; y = 7t Enter the answer in…

A: Here, the given functions are: z=3cos x-sin xy; x=1t, y=7t

Q: Use the Chain Rule to find dz/as and əz/dt. e cos(0), r = st, 0 = V 56 + t6 || dz as az

A:

Q: f(r(t)). dt Use the Chain Rule to calculate f(x, y) = x³ - 5xy, r(t) = (cos(4t), sin(5t)), t = 0

A:

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: Consider the following. w = y? - x = cos(t), y = sin(t) х, dw (a) Find W by using the appropriate…

A: Given, w = y2 – x, x = cos(t) and y = sin(t) and we have to calculate the derivative of w (a). Using…

Q: Find dwdt using the appropriate Chain Rule. Evaluate dwdt at the given value of t.

A: to find dwdt