|(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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: if x²+y²=t-- and x*+y*=t*+÷,prove dy dx x'y

A:

Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: dy Find - for y = du dy du = = [19+ √9 +10t2 dt. 0

A: given y=∫0u9+10t2dtTo find: dydu

Q: (c(2z+y), %3D ue of c in the joi F of W.

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Q: -aluate tan t sec? t dt

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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: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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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: f(x) cos (at) if t 20 %3D 0 if t<0

A: Given: f(x)=cos αt if t≥0o if t&lt;0

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

A:

Q: J. In (T/2) cos ey dx dy In (/6)

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Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

A:

Q: Find the solution for the damped motion. my'' + cy' + ky = 0 with m = 10, k = 90, y(0) = 0.16,…

A: The differential equation of the damped motion is  my''+cy'+ky=0 with m=10, k=90 and c=10 That…

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

Q: A particle was following the trajectory r(t) = (e', sin (2t), t), but it starts flying tangentially…

A: SolutionGivenA particle was following the trajectory r(t)= (et,sin(2t),t) , but it starts flying…

Q: if x²+y²=t-- and x*+y*=t*+=,prove dy X t dx 3. ху

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Q: If y = t“, then dy 4t³. dt

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Q: Find u+ Hy:given that u(x,y) s tan(x+ux+ 11y") 11- x2-y?

A: The partial derivative of a multivariable function with respect to a variable is the derivative of a…

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

A:

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: Find e + Uy, Given that u(x,y) tan(x+11Xy+11y") .t/ - *א- w

A: Given ux,y=tanx+11x2y2+11y411-x2-y2

Q: f(t) = t/ 4t2 + 1, sin(t) cos² (t), for t eR t2 +1

A: In this question, we find the equation of tangent line at t=0 for the given curve f(t) and in the…

Q: Find ds/dt when u = 3pai/2 if s = cos u and du/dt = 5.

A: Given,

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

A:

Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

A:

Q: Use the Chain Rule to find dz/ds and dz/dt. Z = tan(u/v), u = 3s + 6t, v = 6s - 3t dz ds dz at Need…

A: Given z=tanuv , u=3s+6t , v=6s-3t

Q: dy %3D xp

A:

Q: S(1- cos )´sin ź dt, u = 1 – cos 4. U = V5x+8' dx ,u 5x + 8

A:

Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

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Q: find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)

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Q: Let f(x, y) = 7e2" sin(5y) af af dy

A: We can make it easier for you

Q: The vector parametric form of the tangent line to r(t) = (3t², ¿, t – 1) at t = -5 is

A:

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

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

Q: For time t > 0, the position of a particle moving in the xy-plane is given by the vector (, et).…

A: Position of particle = (1/t, e3t) Velocity = derivative of position of particle = (-1/t2 , 3e3t)

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

A:

Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: d²y csinx Find if t Vt2 + 5 dt + sinx = y – x secx dx2

A: We will first find the first order derivatives using Newton-Leibnitiz theorem. The , we will find…

Q: Given a particle is moving in a curve r(t) = cos  7t i + sin 7t j +  8t k. Find the tangential…

A: Given a particle is moving in a curve, r(t) = cos  7t i + sin 7t j +  8t k. To Find the tangential…

Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

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

A:

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: dy Find -5 y%3D(2+cos4t) dy dt

A:

Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

Q: 7. Let F = (2x sin(y)e", x² cos(y)e*, z² sin(y)e*). Find along the path c:T = (sin(t), t, cos(t))…

A: F=2xsinyez, x2cosyez, x2sinyez curlF=ijk∂∂x∂∂y∂∂z2xysinyezx2cosyezx2sinyez⇒curlF=0 So, F is a…

Q: 4. If a particle moves in the xy-plane so that at time t its position vector is sin 31 ,3r2 find the…

A:

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…

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.