Find R(t) if R′(t)=⟨sint3,cost2⟩ and R(π)=⟨12,12⟩.

Q: dz Use an appropriate form of the chain rule to find dt z = 9x10y%; x = t10, y = t6 Enter the answer…

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Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: Find dy/dæ in terms of t if x =t – t°, y = 2+ 4t dy/dx =

A: The differentiation of parametric form of functions can be done by using the formula,

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 ,…

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

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Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Given: y=7x-1 We know that ddxxn=nxn-1                                                       ..1

Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt

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Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: use the chain rule to find dy/dx y=(u+1)2;u=1-x

A: Given:The chain rule of differentiation states that:Applying the derivative with respect to x and…

Q: dw where w = cos 8x sin 3y, x=- dt 5. and y=t". Use the Chain Rule to find 2

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Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: If y = t“, then dy 4t³. dt

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Q: Find dy if x=t+6f and y= dx 2 5 at t=1 +

A: We have to find dy/dx

Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: Compute dy/dx using the chain rule in formula. State your answer in terms of x only.  y = u3>2, u…

A: Given equations - y = u3+2           .....(1)                                                  In…

Q: SxY (@) = 0 and Sx (@) =0 if X(t) and Y(t) are orthogonal.

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Q: dz dz and of the function xsin(y+ z) – xy + z² = 2y. ду -. Find the əx

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Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: Find the differential of the function. u = 2x3 + 7 du = | 0 %3D

A: Given, To find Differential of u=2x3+7

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: |dx + N(x,y)dy = 0 x² + y,

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Q: E(x)三ㄧ-rx.VY.tmdt. Į nd Eicx) Let

A: Since f(t)=sqrt (4-t^2) is even function , so we use the property of definite integral shown on…

Q: dw if: dt Q1) Using the chain Rule to find w = xy + 3z, x = sint, y 2 cost, z=t (x2 +)

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Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(xe^y) .

A: Solution:

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: Use the chain rule to express dy /dx in terms ofx and y y = sin t and t = cos x where t = 0

A: using chain rule

Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

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Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: Find the differential of the function. z = 7t − 7/t2

A: zt=7t-7t2

Q: Ex2: Solve by using Laplace transform y'-x = et • x'+y = e=t, where, x = 0, y = 0,

A: The given system is, where initial condition is x=0, y=0. Now taking Laplace transform of equation…

Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: Find dy at the point t = 5. c(t) = (t4, t³ – 3) * (at t = 5) = dy dx

A: Given that, c(t) = (t4, t3, -3) To find dcdt t = 5

Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: Solve for y(t) where y(t) + 2 / a – u)y[w)du = t.

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Q: y? = = CX Find the orthogonal trajectories of x2 +

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Q: 2. Find dy where y = v3x3 +4x + 1.

A: Given y=3x3+4x+1

Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

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Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

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Q: Use the chain rule to find dz/t. z = x² + y² + xy, x = sint, y = et

A: Here we will find dz/dt,

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Find the tangent plant to f(r, y) = x² + 3ry + 5y² at the point (1,2).

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Q: ,use the linearity of L   determine L[f]. Q. f(t)=sinh bt, where b is constant.

A: Given, f(t)=sinh(bt), where b is constant To determine L[f].

Q: Find df/dt using the chain rule and direct substitution. f(x,y) = squareroot(x2 + y2) , where y =…

A: Given f(x,y)=x2+y2   andy=t2  ,  x=t

Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…

Q: íf was T'fz (R)→R Linearidentifier grand father ♡ Kert ☺ Im T

A: Here given that a linear identifier T :ℙ2ℝ→ℝ3 defined by Ta+bx+cx2=a, b, a+b. We have to find Ker T…

Q: Find the orthogonal trajectories of x2 + y? – 2cy = 0

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