Implicit differentiation Use implicit differentiation to finddy/dx. . sin x + sin y = y

Q: Find the derivative of the trigonometric function. y =  3(1 − sin(x))/2cos(x)   y' =

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Q: Use Theorem 1 to derive the formula.

A: Given  ddxsinx=cosxddxcosx=-sinx The trigonometric identity used here is  cot x=cosxsinxcosecx=1sinx…

Q: e implicit differentiation to find an equation of the tangent line to the devil's curve,defined by y…

A: Follow the procedure given below.

Q: Find the derivative of the function given below. k(a) = sin (a) cos"(a) k'(a) =

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Q: Derivatives of Trigonometric Functions ddx[sec x] = sec x tan x

A: We have to prove the derivative: dsec xdx=sec x tan x We know the trigonometric identity, cos x sec…

Q: Derivatives of Trigonometric Functions ddx[tan x] = sec2 x

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Q: d 1 11. (-) dx x A.

A: The given function is f(x) = 1/x f(x + h) = 1/(x + h)

Q: Second derivatives Find y′′ for the following functions. y=sec(x)csc(x)

A: Given,           y=secxcscx

Q: Implicit differentiation Use implicit differentiation to finddy/dx. y = xey

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Q: y = sec*0 – tan*0

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Q: y = Arctan?(x³)

A: We have to find dydx for y=arctan2x3.

Q: Use implicit differentiation to find ∂z/∂x and ∂z/∂y. x - z = arctan(yz)

A: Consider the provided question,

Q: y : (x² – 3x)³, find y'" х

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Q: Directions: In implicit differentiation, we differentiate each side of an equation with two…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Calculating derivatives Find the derivative of the followingfunctions.

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Q: d 3 dx `x

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Q: Second derivatives Find y″ for the following functions. y = tan x

A: We first find the first derivative

Q: Using implicit differentiation find dy/dx if e^x-y=cos y

A: We have, ex-y=cosy   In implicit differentiation of a function of 2 variables, we differentiate the…

Q: ∫ sinx √cosx dx

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Q: ycosx + xcosy = 2 , find y' %3D

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Q: Derivatives of Trigonometric Functions ddx[csc x] = −csc x cot x

A: Derivatives of Trigonometric Functions :    ddxcscx=-cscx cotx

Q: Calculating derivatives Find dy>dx for the following functions.

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Q: 6. Implicit Differentiation. Consider the curve given by the equation 2x² + y³ = 5xy. %3D dy a. Use…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: ,3 8. 4 cos (x) sin (y) = 1

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Q: f (x) = sin (4x + 7x*)

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Q: Directions: In implicit differentiation, we differentiate each side of an equation with wo variables…

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Q: Implicit differentiation Find y′(x) when sin xy = x2 + y

A: Given, sinxy=x2+y                             ...(1)

Q: (a) Use implicit differentiation to find all points on the curve where the tangent line is…

A: a). Given,

Q: sin(x) Find the 3rd derivative of y =

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Q: y = sech(x² + 2); y ||

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Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx.

A: The above problem can be solved using chain rule. The chain rule states that for three functions f,…

Q: 2. у%3D cos ? (2х — 1)

A: dy/dx = -2sin(4x-2)

Q: Calculating derivatives Find the derivative of the followingfunctions.

A: Given:  y=1-sinx1+sinx

Q: Find the derivative of the function. y = cot2(sin(θ))

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Q: Derivatives of Trigonometric Functions d (sin x) = cos x dx

A: Topic = Derivative

Q: Using Trigonometric Functions  (a) Find the derivative of the function g(x) = sin2 x + cos2 x in two…

A: a)Given a function, g(x)=sin2x+cos2x Find the derivative of the function in two ways, Now…

Q: IV. Higher Derivatives sin(x) 1) Find the 3rd derivative of y

A: Given: y=sinxx For finding third derivative of given expression, we need to find first derivative…

Q: 6. y = Arccos ()

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Q: d (2х* Зх 3) dx

A: Using basic differentiation formulae: ddx2x2    3x     3=d2x2dx     d(3x)dx    d(3)dx

Q: Implicit Differentiation. dy There is need to simplify. da Use implicit differentiation to find a.…

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Q: y= Arctan

A: The function is y=Arctan2x3.

Q: sin Find the first derivative of 1-2 cos x

A: Given: sin(x)1-2cos(x)

Q: 2. Determining Advanced Derivatives of Trigonometric Functions A. f(x) = sin x + cos x B. f(x) = sin…

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

A: Given : To find out relative maxima and minima we need to take first derivative and find out…

Q: Derivative f(theta) = sin(theta) cos2(theta) - (cot)/(theta) + 1

A: Here, fθ=sinθcos2θ-cotθ+1

Q: Higher-order derivatives Find and simplify y″. x + sin y = y

A: Given:  x+sin y =yTo…

Q: d 7.- (2) dx

A: The differentiation of a constant term is zero. Whereas. if constant term is with variable then its…

Q: . Implicit differentiation Use implicit differentiation to finddy/dx.

A: Given : y = x+1y-1 ...(1) To find : dydx Equation (1) becomes y(y-1) = x+1 differentiate w.r.t x on…

Q: Direction: Find the first derivative of the following functions: 1. y = sin (2x)- cos (2x) 2. y =…

A: 3. y=tan(3x) cot(3x)4. y=cos x1+sin x6. y=xarcsinx+1-x2