er a function y = g(x) whose curve is given by the equat dy dx y Cos x 1ow that: 4y-sin x rite an equation for the line tangent to the curve at the r0< x < r and y > 0, find the coordinates of the point w nt: cos(t) represents the x-coordinate of the unit circle;

Q: #2/H B ) Find the equation cof the tangent line to the graph of f at the given pont f(s)=(…

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Q: dy Findby implicit differentiation. dx x*y - 8xy + 3xy? = 9 %3D Find an equation of the tangent line…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Q.NO.3: dy i. Find using logarithm differentiation dx 5 x - 1 x + 1 ii. Find a point on the curve y…

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Q: 47–48. Higher-order derivatives Find y'. y", and y" for the following functions. 47. y = sin Vĩ 48.…

A: 47. y=sin x

Q: II. A particle is moving along a line with velocity given by the function v(t) = t-…

A: We have to find the position function of the particle at any time t.

Q: Q#3: (i) Find the function with the given derivative whose graph passes through the point P. r'(8) =…

A: r'(θ)=8-csc2θ , (π4,0)r'(θ)= sect.tant-1, (0,0)

Q: 4 sin x Let f(x) = 2 sin.x + 6 cos x Then f'(x) = The equation of the tangent line to y = f(x) at x…

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Q: The where c Is a constant, is equal toC 7. If y = 6e5, then y' = 30e*. The derivative of a product…

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Q: Consider the interesting curve below which is described by the equation cosh(sinh(v))=V1+x?…

A: Question is solved.

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Q: 25. Find an equation of the tangent line to the graph of the function at the given point. Function:…

A: y = -2x +3π/2 -1  Hence option (a) is correct .

Q: 3. 4ln(Arctan x) = 1- y

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Q: dy at this point. Find an equation for the line tangent to the curve at the point defined by the…

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Q: 3 The relation y +7xy - 6x° = 14 defines y implicitly as a function of x. dy (i) Use implicit…

A: Implicit differentiation

Q: dy Find by implicit differentiation. dx = 4 + In (x +y) , y -x Select the correct choice below and…

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Q: Q1: Find the following: a. Differentiate with respect to the parameter t x = sin?t, y = cos²t b.…

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Q: a. Differentiate with respect to the parameter t x = sin?t, y = cos²t b. Find the derivative dy/dx…

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Q: dy 3. (A) Find for the following. dx (a) x = 5 sin 6t + 4 and y = 5 cos 6t + 3 (use parametric…

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Q: 5. Consider the curve defined by x² + xy + y² = 1 The graph of the curve is shown below. dy (a) Use…

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Q: 2x ind the derivative of: 2e cos(8x). [Hint: use product rule and chain rule!] se e^x for e*. ow,…

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Q: Q1. Find ý of the function x? – e2x+3y – In(xy3) = 0. %3D Q2. Use the definition of the derivative…

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Q: Find dydx implicitly for the equation sin y = x. Then find the largest interval of theform −a &lt;…

A: The given equation is sin y=x. Differentiate both sides of the above equation with respect to x-axis…

Q: dy The derivative of e'In(y)=cos(xy) is equal to dx s(x.y) 8(x.y)* What is the value of 8(x,y) if x=…

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Q: x²+3 Suppose y = and x = sin (u)ln (u) a. Determine dy using the first principles definition of a…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: dy without first solving for y. dx Use implicit differentiation to find y? 1 36 36 dy dx At the…

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Q: Suppose the movement of an object is described by the position function x = cost + 2 y = sin t + t 2…

A: Velocity vector.

Q: Q1: Find the following: a. Differentiate with respect to the parameter t x= sin't.y = cos²t b. Find…

A: a) given that x=sin2t , y=cos2t differentiate it wrt t find dxdt and dydtb) given that x=sin2t ,…

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A: Given,                 dydt=y+12t and when t=1 then y=3

Q: (5) cosx (C)tanx . (D)sinx. (D) 10 5: The average rate of change of f(x) = x² + x on the interval…

A: According to rules, I need to solve only one question when multiple questions are posted So repost…

Q: Suppose that a curve is given by the equation y2=x2+x+1 which defines y as function(s) of x Find…

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Q: 4 sin x Let f(x) = 2 sin x + 4 cos e 4 Then f'(x) = (sin (z) + 2 cos (2)) The equation of the…

A: We are given,                 And we have found               . So, the slope of the tangent line…

Q: Find dy/dx, using implicit differentiation. HINT [See Example 1.] y In x + y = 9 Compare your answer…

A: We are required to find its implicit differentiation. After we have to differentiate if for y as a…

Q: Let f(x) = 2 · sin(x) – 5 · cos(x). What is the slope of the tangent line to the curve y = f(x) at x…

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Q: II. Find the derivatives of the following functions. No need to simplify your answers sin a.…

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Q: (1)Find dy/dx when 3x2+3x3y - 5y3 = 20  dy/dx= (2)The slope of the tangent line to this curve at…

A: The function 3x2+3x3y-5y3=20. We have to find the derivative, slope of the tangent line at (2,2) and…

Q: Consider the following. x2 + y2 = 9 (a) Find two explicit functions by solving the equation for y…

A: The given function is x2+y2=9

Q: II Find the second derivative(y") of the following functions and simplify the final results. 1.…

A: Since you have posted multiple questions, we will answer the first question. If you want the…

Q: Consider the interesting curve below which is described by the equation cosh(ainhn-(v*))-Vi+x dy…

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Q: dy for the implicit function x +y -2y = 3. Then find the equation of the tangent line at the Find dx…

A: use differentiation for finding the slope and then use it for finding the equation of tangent line.

Q: (a) Use the definition of the derivative to find the derivative of f(r) = V9- r. %3D (b) Find or y'…

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Q: Q1: Find the following: a. Differentiate with respect to the parameter t x = sin?t, y cos²t b. Find…

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Q: 1 y + x In x Find equation of the curve whose slope at any point is equal to 1 - and which In x…

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: Given a point is moving along the graph of the given function at the rate of dxdt. Given function is…

Q: L(0) = [B] Now, find the derivative, L'(0). Type theta for 0. L'(0) = [C] Once you find the value of…

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Q: e) GIVEN: The graph T: cosy + sin 2x=D1, xE[0, 폭.yE-,풀| = 1, xe Express y' in terms of x and y Find…

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Q: 5) Find the derivative of h(0) = tan 50. d 6) Find dy (cot y).

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Q: which is described by the equation cosh(sinh *(v²)) = /1+x² dy (your expression will contain both x…

A: It is given that coshsinh-1y2=1+x2. We have to find the differential equation y'=dydx. We have to…

Q: 2. A particle is moving along a horizontal line. The velocity (in cm/s) of the particle after t…

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