(3) Let 4 = x²y² + x sin y, find 2 dy in terms of x and y; dx (4) Find the equation of the tangent line of y = /1+4 sin x at the point (0,1).

Q: 2. Find dy/dx (a) x = 5 sin 16t + 126 and y = 5 cos 16t + 13 (use parametric differentiation) (b)…

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Q: Let y = tan(2x + 2). Find the differential dy when z = 5 and dr = 0.2 Find the differential dy when…

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Q: Let y = tan(4x + 6). Find the differential dy when x = 3 and dx 0.1 %3D Find the differential dy…

A: Explanation is given below...

Q: (a) | (2x cos y + sin x) dx 6. */2 (b) I| (2xcosy+ sin x) dx dy

A: Solving integral

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

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Q: Find dy/dx and d-Y/ dx" of x = 2t" 3, y = 1. Give the equation of the tangent line at t = 2.

A: We have to solve

Q: (b) Find the equation of the tangent line to the curve 8x²y3 – 5x2 + 7y3 = 10(x – 3y), at the point…

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Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: 2. Consider y = cos(2x). 2.1. Find Y dx 2.2. Determine an equation for the tangent line at x 0.

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Q: (2-4t) sin(팔) V17- cos(27t) 1. Given f(x) = dt, find the equation of the line tangent to the graph…

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Q: ( 2x – sin y) dx – (x cos y) dy = 0 -

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Q: Find dy/dx at x=0 if y= Cosu and y--3x

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Q: y = x * (sin 1x)² – 2x + 2v1-x² * (sin-1x), Find dy dx

A: Given that equation of y and we find dy/dx. We know that d(sin-1x)/dx = 1/√1-x2. And d(xn)/dx =…

Q: Find the differential dy of the given function. y sec² x x² + 2 dy sec²x(x²+2)tan x-x (x² + 2)² dx X

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Q: Determine the equation of the tangent line to the graph of g(x) = mz [1 – sin(ne')]dt at the point…

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Q: Find the 3rd derivative of the function given by the parametric equations x=1+sint, y=t−cost at t=0.

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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: 2. Calculate the derivative dy for the parametric equation x = t² + ³ + ln(4t+1), y=e5t² giving your…

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Q: 2 (b) - 2y dx +(2y tan'(x )-2x +sinh (y))dy = 0

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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: . z=tan 2x dx From their derivatives find

A: Question is solved.

Q: Find the differential of the function. y = 0 sin(60) dy =

A: To find the differentiable of the below function. y=θ3sin6θ

Q: Find the equation of the line tangent to the cardioid r = 1+ sin(0) at Ô0 =

A: Given that,, Here, differentiate w.r.t. ,we get, We know that, To find: equation of the line…

Q: Consider y3-2x2=1+sin(xy)   a) Use implicit differentiation to find dy/dx.   b) Find an equation…

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Q: Find dy/dx of y=sin-!x+cos -!x dy/dx is Blank 1.

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Q: Find the equation of the tangent to the curve at t = 0

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Q: Find the value of dy/dx at (1,0) of 2re" – In() = 4y² + 2a sin

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Q: Find the derivative of y with respect to x. y = In (tan -1(2x4)) dy %3D dx

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: Find an equation of the line tangent to graph of y =x2 + sin (Ex) at x=-1. A. 2x - y+2 = 0 B. 2x +…

A: To find the equation of tangent line of the given graph.

Q: 2x + 2y %3D 1. Use implicit differentiation to find dy/dx for ey

A: GIVEN ex2y =2x+2y

Q: 1. Evaluate the dy for parametric equations x = 3t³ - 3 and dx y = 3t² - 6t using parametric…

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Q: ey sin x = x + xY %3D

A: Solution:- The given implicit function is  ey sinx=x+xy

Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: Find the differential dy of the given function. y sec² x x² +2 dy = sec²x(x²+2)tan x-x (x²+2)² dx x

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Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: 6. Let y + xy - y = 8x*. a) Find dy/dx using implicit differentiation. b) Find the equation of the…

A: In implicit differentiation, when we differentiate y, we use dy/dx

Q: Let y = tan(3x + 8). Find the differential dy when x 5 and dx = 0.4 %3D Find the differential dy…

A: First differentiate then put the values

Q: The degree and order of the differential 1 dy equation 1+ is 3 dx wy dx

A: Solution

Q: Find dy dx for sin(xy) + y³ = x² + 1 and use it to find the equation of the tangent line at the…

A: use differentiation for finding the equation of tangent line.

Q: Find dy of the function y = cos2 3X + √√Sin x dx

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Q: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

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Q: Can you help me step by step?

A: Given information:

Q: 2 Calculate the (d^n*y)/(dx^n) derivative of the curve with the parametric equation x=lnt, y=t^alpha

A: The given problem is to find the nth derivative of y with respect to x of the given parametric…

Q: dy of xy +y-xy=15 using implicit differentiation. dx 3) Find dy at the point (2,3) dx Hence find

A: To find dy/dx using implicit differentiation.

Q: tan(2x + 2). Find the differential dy when x = Let y : 4 and dx 0.2 Find the differential dy when x…

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Q: Find the differential of the function   y = θ3 sin(6θ)

A: Solution :-