What is the equation of the line tangent to the curve e + cos(x) =1 at the pointG.0) A (B) y=x+ C y=0 D y=x-

Q: Find dy/dx by implicit differentiation. (cos TX + sin Ty) = 18

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Q: 5a?y – y³ = 6x² – 2 a) Find dy/dx by implicit differentiation. b) Find the slope of the tangent line…

A: Given equation is 5x2y−y3=6x2−2 (a) Differentiate 5x2y−y3=6x2−2 with respect to x…

Q: 7. Find the dy/dx of * y = In sin 5x

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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: 12. cos cos (xy) = 1+ sin y

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Q: Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You…

A: given: the function f(x)=-3cos(x) the point is x=-π3

Q: 7) Find dx 4e* dy if y = %3D 8) Find the first derivative of f (x) = sin? (x°).

A: We need to find out : 7)  dydx if y=4exx 8) First derivative of f(x)=sin2(x3)

Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: 13. We know that x = r cos 0 and y = r sin 0, then find the derivative af/ar if 1 f = ? + y?

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Q: - sinx) dx 2. 1. (COSX (ax' +b)*x dx 2. 2/3

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Q: find dy/dx of y=cos2x-sin4x

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Q: Find the equation of the line tangent to the graph of y = arctan (sinh(r)) at z = 0. %3!

A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

Q: dy tan tan x = 0 dx coscos x +

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Q: Find an equation of the tangent line to y sin 2x = x cos 2y at the point π/2 , π/4 . Do not…

A: First we will find Differentiation of given equation to get slope of the tangent line. Now equation…

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

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: 2. Find dy/dx by implicit differentiation: 5x^2y+5y^2x=-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: Find dy/dx in terms of x and y if cos^2(9y)+sin^2(9y)=y+7 dy/dx=   implicit derivative problem.

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Q: What is the equation of the curve whose tangent line passes through the point sec (In x) dx? (1,2)…

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Q: Find dy/dx of y=sin-(1/,). 9x-

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Q: 5. As a particle moves through the first quadrant, its a and y coordinates are functions of time t,…

A: Given tan(theta)=y/x

Q: for (e3x+y2)5 = sin x cos y, find dy/dx. using implicit differentiation. must show all steps

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Q: 4 sin (2x) dx cos (2x)t4

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Q: Calculate the derivative. y = cos 3x In (cos ²3x) y' =D %3D

A: We can find the derivative as below.

Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

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

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Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

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: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: 3/20 What is the equation of the tangent line to the function y = e*- arcsin) at x= 0 ? A) y- -(1+)=…

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Q: Find dy/dx by implicit differentiation 4 cos (7r) sin (6y ) 5

A: We have been given an implicit function and we are supposed to find dy/dx.

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: 8. [(cos'y- sin'y)dy

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Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

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: 1I) (3y cos(3x)dx-sin(3x)dy)/ y 0

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

Q: is The third derivative of y = cos 3 1 sin 27 1 a) y" b) y" =- cos %3D %3D | - 3 27 3

A: The given differential equation is : y=cosx3   -1

Q: Find dy/dx by implicit differentiation. (cos TX + sin ny)³ = 26 dy/dx =

A: Differentiate above equation with respect to x

Q: 2- Find the derivative of y with respect to the Exercises 1-3. = 6 sinh 1- 1 sinh (2x + 1) 2- In…

A: These are the hyperbolic function so use standard form of derivative of hyperbolic functions.

Q: 2- find dy/dx e2x = sin (x + 4y) 3-find an equation for the line tangent to the graph f(x) = x –…

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Q: Find the value of dy/dx at the point (−2, 1) for the function which is defined implicitly by

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Q: The derivative of y = In(sin(ex + 1)) is O y' = -ex cot(ex + 1) the above y' = -ex tan(ex + 1)

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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: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

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

A: Solution :-