&y dy :5 cos t, the third order derivative dt For the function dt3 is 5 cos t -5 cos t -5 sin t cost

Q: dr dy 2x 3x Suppose x and y are functions of a third variable t. If sin2 (x) + cos²(») = and 1, what…

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Q: A particle moves on a straight line with velocity function v(t) = sin ωt cos2ωt. Find its position…

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Q: CoS z 5,⁰ √1+4t2 dt, find F'(x) 11. If F(x) =

A: The objective is to find F'(x).

Q: Let y = sec (3x)V 361 cos (3x) + 646 + 289 sec (3x) , 0 <x< a²y Find at x= 2 12 dx Hint : Before…

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Q: dy For the function dt = 3 cos t, the third dy order derivative is dt3 -3 sin t -3 cos t 3 cos t 3…

A: Find the third derivative of the first derivative  function

Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

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Q: Find the derivative of cos(0)d0. du Jo cos(0)de = cos (w²) · 2w • d de So" cos(8)d0 = cos(2w) • d S…

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Q: dy For the function dt d y is 3 cos t, the third %3D order derivative dt3 O 3 cos t

A: Given: dydt=3cost To find the third order derivative d3ydt3. Solution: We have, dydt=3cost…

Q: dy at the given point. dx Calculate sin² (–5y) = x + y, - %3D 4

A: Given equation sin2(-5y)=x+y and point 2-π4,π4 The objective is to calculatedydx at the point.

Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k.

A: Derivative of r(t) = cos (8t) i + sin9(t) j + tan (6t) k

Q: What is the value of f (5) if f (t) sin (Ta) dt :? 1

A: Given, ∫1xfttdt = sinπxx   We have to find the value of f5

Q: find dy/dt. y = (t-3/4 sin t)4/3

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Q: Q3) Find dy/dt of the function y = cos (5sin (t/3))

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Q: The equation of the tangent to the curve y=4+ sin' x at X=0 is O y = 4 O y = 2 O y = 6 O y = 3

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

Q: COS X dy for y = dx Find the derivative dt . Here, 0 < x < T. V1 -2 0. Enter your answer as a whole…

A: Leibnitz Integral Rule:                      Let ϕ be a function of 'x' and 'z' .i.e, ϕ(x,z).Also,…

Q: dy b) Find If tan2²(2y) – S cost dt = 4 – x2 - dx

A: We find the dy/dx by Leibniz rule.

Q: A particle moves on a straight line with velocity function  v(t) = sin(ωt) cos2(ωt).  Find its…

A: The given velocity function is,

Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

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Q: Find dy/dx. Y = cos (cos x). A sin(cos x) sinx sin x cos x sin x B.

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Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: Find the derivative f (t) = 1- cos t | a. 1 cos t - 1 sin t C. 1– cos t - t · sint (1 – cos t)? b.

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Q: dy Find for y = cos (8at + 1). dt dy dt

A: We have to find out dy/dt for given y

Q: find function y =f(x) Satisty ing given equation. %3D and the prescribed initial candition dy CoS…

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Q: dy For the function dt d°y order derivative = 4 cos t, the third is dt3 -4 sin t -4 cos t 4 sin t -4…

A: Differentiate the given function expression with respect to t twice to find the required value

Q: nd the derivative of (z.x)= X+c Cos (27 X) Point (0,2,1) in the direction at of V=i-sj+k

A: Directional derivative is dot product of gradient and normalised vector.

Q: 3 2 Find for y = dt, where x> 9t+2 dx dx

A: The given function is y=∫0x39t+2dt. Let u=9t+2. Then, du=9 dt. The upper limit will be 9x+2 and the…

Q: rycotx b) Find If cos (2y) – S cost dt = 4 – x? - dx

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Q: If f(x.y)=sin (2x+y) then the derivative f, Is 2 cos (2x+y) a. b. cos (2x+y) c. 2 sin (2x+y) d. 2…

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Q: Assume that x and y are both differentiable functions of t and are related to the equation: y =…

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Q: The third derivative of y = cos 1 sin 27 1 111 a) y" b) y" 27 %3D 3 1 1 c) sin d) y 27 y = - %3D 27…

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Q: A ) Find ſ cos 5t dt dy B) If y = x² +; , x= 2t -5 then find dt

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Q: Assume that z and y are both differentiable functions of t and are related by the equation = cos…

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Q: Assume that x and y are both differentiable functions of t and are related by the equation y = cos…

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Q: dy dy For the function dt 7 cos t, the third order derivative dt3 is %3D

A: derivative with respect to t first oder derivatinve dydt is ddt(y). (which is given in the…

Q: The third derivative of y = sin(2.x) is (A) None of the given choices B y" = 8 cos(2æ) © y" = -8…

A: This question is related to differentiation, we will solve it using given information.

Q: at and ду ду Suppose that 3x - 4y = t and y =t sin 0. Find dt

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Q: Q6:- Show that R = (sin t)i + (cos t)j + v3k has a constant length. And R(t) is orthogonal to its…

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

Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k. %3D dr dt

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, t2), 0 sts 1. (Round your answer to…

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Q: cos(x) If f(x) = ["(@) "g(x) V1 + t3 dt, where g(x) = S [1 + sin(t²)]dt, find f'(;). 1 %3D

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Q: dy Find the derivative for the function x = sin 2t, y = – cos t at the point t = dx 6.

A: Using derivatives of parametric equations.

Q: The velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for all t.…

A: given the velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for…

Q: Find dz/ðx , dz/ðy at the point (1,1,1) if x³ + z² + ye + xz cos y = 0

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Q: We know that x =r cos 0 and y =r sin 0, then find the derivative af /ər if 1 f = x2 + y2

A: Given f = 1x2+y2  and x = r cosθy = r sinθ Thus f = 1r cosθ2+r sinθ2= 1r2 cos2θ+r2 sin2θ=…

Q: dy = 5 cos t, the third order derivative dt dy For the function is dt3 O 5 sin t 2-5 cost on O-5 sin…

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Q: H.W Ex.(8) Show that the functions f(x) = sin' () and ga)=2 tanv メ+) have the Same derivative.

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Q: Q2: find dw/dt at given value point for the following function x= cos°(1), y = sin²(1).= =-. 1 at t…

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Q: dw b) If w = (x + tanx). (Vx – 1), and x = tan (cost) find dt

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