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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: 3. Find dy, where; a) cos(ry) - e 2 elx+y). b) ė?+ Ptany =4, u= xlax (use chain rule)

A: We have to find the derivative

Q: Consider the system i = f(x)+ g(x)u iere sin x2 f = COS x2 g =

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Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

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Q: (b) u = Vt² + 2vt3 - 1 tan I (d) y = sec I VE-1 (f) y = VI+1

A: Since you have asked multiple subpart, as per our guidelines we are supposed to answer only first 3…

Q: Transform F(s) (giving you cos 5t + t³

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A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: dw Use an appropriate form of the chain rule to find dt w = In(162? – 4y + 3z³); 1 = ti, y = tỉ,…

A: Topic- differentiation

Q: Use the Chain Rule to find dz/as and dz/at. 2 tan(u/v), u = 5s + 2t, v = 25 - St

A: Proceed as shown

Q: (a) i. Find Re{sec (x + iy)}.

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

Q: et u = e Sin P= sin sc Lind su using chain Rule

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Q: and as Use the chain rule to find sin(6) r = st, 0 = s + t3 dz as

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Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

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Q: Evaluate I = fc (sin(x) + 4y) dx + (9x + 7y) dy for the nonclosed path ABCD in the figure.

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Q: Find aw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) X = s + t, y…

A: we have to find partial derivative by using chain rule

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: QS A) Find IF y = - Ve IF y =-Vt and t sinx

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Q: Find and ди ди using the chain rule. w(x, y) = 14x²y², x = e" cos v, (u, υ) ди (u, υ)

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Q: Be w = (u2 + v2)3/2, where u = e-t sin(θ), v = e-t cos(θ), calculate: ∂w/∂t and ∂w/∂θ

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Q: Use the Chain Rule to find dz/əs and dz/at. z = tan(u/v), u = 8s + 3t, V = 3s 8t az as az Ət II

A: Given data: *z=tan(uv) *u=8s+3t and v=3s-8t The partial derivative of z with respect to s is given…

Q: b) Use chain rule 1 - arctan u, where u = e* y =

A: Given y=1u - arctan u, where u=ex apply derivatives on both sides…

Q: Use an appropriate form of the chain rule to find and if z = xe" , x = 2uv , ди y = sin(uv). You…

A: By using the definition of  chain rule for two independent variables we find the value of ∂z∂u, and…

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

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Q: TIJY sin /x dx dy by using the transformation u= Vy. v= Vx ? 0 0

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Q: a2f Compute Je Je дх' ду f(x, y)= x²y² – sin 2 + xe" and : дхду

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Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

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Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

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Q: Use appropriate forms of the chain rule to find dz/ðu and dz/dv. Z = cos x sin y; x =u – v, y = u² +…

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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

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Q: Express in the form x + jy (3) sin(t/4+j2)

A: Complex Number Question

Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

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Q: ди ди then x +y = u. 31. If u = Jy² - x2 sin-

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

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Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: dy If y = tan t , x = tan? t ,Find by using Chain Rule dx at t =

A: Let the two functions are xt and yt. The chain rule to find dydx is given by the following formula.…

Q: Find F(s). F(s) L{cos(6t) U(t - π)}

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Q: Use the Chain Rule to find az/ds and az/ôt. z = tan(u/v), u = 3s + 6t, v = 6s - 3t az as az at II

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Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

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

Q: Calculate the Cauchy principal value. 8 COS X V.P. Leta -dx, (a > 0). (a²-x²)

A: We solve by using residues.

Q: Use the Chain Rule to find zz and zy given sin(u) tan(v), u = 3x + y, and v = x – y. %3D

A: Given z = sin(u) tan(v)where u = 3x + yv = x - y

Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: If w = Vr + y² + zª where r= sin(0), y = cos(@) and z = Use the Chain Rule to find tan(@). dw when…

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Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: Find LT for f(t) = sin²(wt), f(t) = cos²(wt) %3D %3D

A: We need to find the Laplace transform of ft=sin2wt and ft=cos2wt Now, before finding the Laplace…

Q: Let z = f(x, y) where g = e° cos t and y = e° sin t. Use the Chain Rule to show: z = e

A: Let z = f(x, y) where x = es cos t and y = es  sin t. We will be using the chain rule to show,…

Q: Use the Chain Rule to find ôz/ds and ôz/ðt. z = tan(u/v), u = 5s + 9t, V = 9s – 5t az as az at

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Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Q: Evaluate 2.xyz dx + x²zdy +x²ydz over the path r(t) = (t², sin(nt/4), e'“-2') for 0 <t<2.

A: The given integral is: I=∫C 2xyz dx+x2z dy+x2y dzOver the path:  r(t)=t2,  sinπt4,  et2-2t    for…