Q.1 (i) calculate the following: lim(4x' –3x² –15) x' -4 lim x-2 (ii) An equation of a curve is defined as: xsin 2y = y cos2x Use implicit differentiation to determine: dy the gradient at the point (iii) Use the parametric equations x = te“ and y =1+e" to evaluate- dy

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: 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: (1 )  (a)  Find two positive numbers x and y whose product is maximum and 2x+y=100. ( b )  Find…

A: a. Given The product is given by P=xy Plugging the values: For P to be maximum, the derivative…

Q: Consider the curve described by the relation y + eV= x* - x² + 1. Find an equation of the tangent…

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Q: Can you help me with this problem step by step?

A: Given:

Q: Find dy/dx by Implicit differentiation. x = 9 In(y-15), (0, 4) dy %3D Find the slope of the graph at…

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Q: A) find the derivatives for the following: 1) y = In(In(sin¯'(e?r))) – 5-Inx 2) Y=sech-1(log, 93*) +…

A: Chain rule for differentiation: Let y=fghx then dydx=ddxfghx=dfghxdghx×dghxdhx×dhxdx Equation of…

Q: 1. Find the derivative of the following using implicit differentiation. TYON b. BARZ c. y = sec(x +…

A: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question and…

Q: Can you help me with this problem step by step?

A: Given equation is

Q: gives the first derivative of a continuousfunction y = ƒ(x). Find y″ and then use Steps 2–4 of the…

A: y'=cost,    0≤t≤2π

Q: Can you help me with this problem step by step?

A: To determine the first and second order implicit derivative of the equation.

Q: 1: A)find the length of the curve y=3(x)/2 – 1 from x=0 to x=1 ? B) Prove that: cosh (x + y) = coshx…

A: A) Length of the curve is y=3x32-1 B) Trigonometric function

Q: #15) Determine y' a.y=sin 2x b. y = x² sinx co y = sin(-x) Determine #16.> d.) y = cos x sin x e-> y…

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Q: 1. Find the derivatives of the given functions. a. y= arccos(x b. y = In (arctan x) c. y= csc (2u+1)…

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Q: 3. Find the slope of the tangent line to the curve y = +2 x*+4x+7 4. Determine and 4 of y = (5.x² –…

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

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Q: Can you help me with this problem step by step?

A: The given equation is x = cot y.Differentiate both sides with respect to x.

Q: Find y' by implicit differentiation. cos(x) + √y = 2

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Q: Q1: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i – 3j…

A: (a) Given S=ln(2x+3y) Differentiate S partially with respect to x and y Sx=22x+3y…

Q: dz Find and dz by implicit differentiation, and confirm that the dy results obtained agree with…

A: Let f(x, y, z) =yex-5sin3z-3z

Q: what is of point Fyl-2,0) fexsy)=(x3ーy+g)s

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Q: dz Find dz and by implicit differentiation, and confirm that the dy results obtained agree with…

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Q: (4) (a) Find dv/dx by implicit differentiation: cot y = x – y (b) Use implicit differentiation to…

A: Take derivative with respect to x and express dy/dx in terms of x & y.

Q: 1. b. Find the differentiation of the following functions: i. y = 2 tan(1 – 2x) + ex²+x -

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Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: I Find the second derivative(y") of the following functions and simplify the final results. 4. y =…

A: 4 y = xcosx now fist derivative y' = x(cosx-1)cosx(-sinx) y' = (-1/2)sin2x x(cosx-1) now again…

Q: 1. Find dy/dx by implicit differentiation.  x sin(y) + y sin(x) = 7  y' = ?

A: Note:We are authorized to answer one question at a time, since you have not mentioned which question…

Q: 2. Given that arcsec 2) + (x² – y²)² = 2. (a) Find dy using implicit differentiation. dx dy usino…

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Q: (a) Find the equation of the tangent line to the curve x = e', y=e %3D at t = 1 without eliminating…

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Q: 1. b. Find the differentiation of the following functions: i. y = 2 tan(1 – 2x) + e*²+x ii. y =…

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Q: dz Find and dz by implicit differentiation, and confirm that the dy results obtained agree with…

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Q: 3. Consider the curve given by r = 2+2 cos (0) where 0<0<2n. Find the slope of the tangent IT line…

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Q: Can you help me with this problem step by step?

A: Given:

Q: 14. Find the derivative of y = e cosz %3D A. y' = -ecosx sin z B. y' = elinx cos x C. y' = -etinx…

A: Given,y=ecosxdifferentiating both the sides w.r.t. xdydx=ddxecosxUsing chain…

Q: I ind the second derivative(y") of the following functions and simplify the final results. 1. y = x3…

A: Given y=tan-12+x1-2x To find y'':

Q: 2. : Consider the function ry + cos y + x 2+ xy. (a) Find the derivative, dy/dx. (b) Find the…

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Q: Q1: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i…

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Q: 14. Consider the curve defined by x2y2 - 3x2 - 6y2 0. dy a. Use implicit differentiation to find :…

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Q: Find the slope of the tangent line to the curve y = g²+4r+7 at the point (0, 3). 7a+2 Determine da…

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Q: Find and using implicit differentiation. az Leave your answers in terms of x, y, z, and w. In(4r² +…

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Q: Can you help me with this problem step by step?

A: Differentiating implicitly with respect to x on both sides. Solving left hand side first.

Q: 23) Find the SLOPE m = at the point (2, 0). [Hint: sin 0=0 and cos 0 =1] A) 2 of a tangent line to…

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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: Suppose that x² + y² = 82. dy (1) Use the method of implicit differentiation to find dx dy dx (2)…

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Q: 2. Prove the formula of the derivative of y = cosec-f(x). d²y and dx2 of the parametric equation…

A: 2. Given y=cosec-1f(x) we need to find the derivative. cosec y =f(x)   (1). But we already know the…