b. Find first and second derivatives (dY/ dX, d'Y / dX² )of the following functions aX² +1 (а) Ү - (b) Y- (ax + b)(vx-1); (c) Y-(1+ sin x)(1-cos x) X-1

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x² – 1)³(x² + 3)² x3+4x…

A: Given functions to be differentiate are    1.   y=x2-2x3+4x    3.  y=x2-2x      we will make use…

Q: f(x) = acos(b\x) x2 COS

A:

Q: Find the partial derivative. z = sin(9x°y – 10xy²)

A: Given: z=sin9x3y-10xy2

Q: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

A:

Q: 4. Find by implicit differentiation of x sin(y) = y cos (x) dx

A: The given problem is solved below in detail.

Q: Find the third order derivative of y = In(cos(2x))³. A. y' = -40sec² (2x)tan(2x) B. y' = -80sec?…

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Q: Find the derivatives of the functions  1. y = x2 cot 5x    2. y = x-2 sin 2(x 3)

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find the partial derivative of the given In[y? sec(x²y²)].

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Q: (a)Deduce the 1$, 20d and 3rd derivatives of y = cos²x.

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

Q: 2 Suppose that x and y are related by the equation 4x² - 3y² = 5 and use implicit differentiation to…

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Q: Find the derivative of y with respect to x if y=∫0ln(3x) sin(6et )dt

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Q: Find the derivative. y = 3t cos (t6) dt Select one: 3 A.6x cos (x ) 3 3 B.3 cos (x ) - 3^/x sin (x )…

A: The solution are next step

Q: 3. Find the derivative y'(x) implicitly. cos²x + cos²y = = cos (2x +2y)

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Q: Q1) Use implicit differentiation to find dy/dx if x cos(3x + 2y) = y sin x

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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 derivatives of the functions y = sin-1√1 - u2, 0 < u < 1

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Q: Determine the derivative of y=tan(cos-(4x)). -1 A y'=. 4XV1- 16x2 None of the given choices -1 y's…

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Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: Find the 3rd derivative of (1 + 2y)³ + eª (sin² y) - 3y cos(e=? )

A: Given data (1+2y)3+ex(sin2y-ycosex2=3y and find 3rd derivative or d3dx3=?

Q: 14. The first derivative of y = arcsin4x is а. -4 b. -4 C. d. V1- 16x? VI- 4x2 V1– 16x? /1– 4x* -

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Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

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Q: 2. Find the derivative of: (a) A(x) = [ 1n | In(sin(3t)) dt (b) A(x) = L, In(sin(3t)) dt

A: According to the Leibinitz rule :

Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: Find the derivatives of: d/dx (ex-e-x/ex-e-x) And the derivatives of: f(x)=ln((2x+1)3/(3x-1)4)

A: the given expressions is: dex-e-xex-e-xdx the given function is: f(x)=ln2x+133x-14

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

A:

Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

A:

Q: Find the derivative of y with respect to x. y = 6x° sin -1 (6x) + /1- 36x° dy dx II

A: Given function is By using product rule of differentiation, we get

Q: 22. Find the derivative of y = arcos(4x) with respect to x. - 4 4 - 4 - 4 В. 1-4x2 С. Vi-(4x) A. D.…

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Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: Find the derivative of the function sin(x) In(6+4v) dv cos(x) y y'(x)=

A: The given function is,

Q: 6. Find the derivative of function. a) y = (x - 1)ā + 2x2-4x+7 b) y = cos* 3x * arcsin 3x2 |3D 3 c)…

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Q: Find the derivative of the function. "sin(x) In(7 + 9v) dv /cos(x) y'(x) =

A:

Q: 4. Find the derivative of the functions. (2x2-3) a. y = (x247)5 sin x b. y = 1+cosx

A:

Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

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Q: 4. Use implicit differentiation to find dy/dx. (a) ye" = x" + 1 In x (b) ymz = x"

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Q: Find the derivative. d | dx + 0 OA. x³ sin (x¹) +5, ○ B. sint dt C. 4x³ sin (x4) - cos (x4) - 1 D.…

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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 the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 2. Y= 2 Arccos (1-)+ v4x – x?

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Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: Find the third order derivative of y = In(cos(2x))5. %3D A. y' = -40sec² (2x)tan(2x) %3D В. у' 3…

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Q: b) Use implicit differentiation to find dy/dx of y² : X-1 x+1

A: Using implicit differentiation &amp; quotient rule.

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

A: Let z= 6x^2+1 Substitute that. Then take d/dx on both sides.

Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

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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: 5. Find dy/dx using implicit differentiation given x²y³ + cos y = 0.

A: Definition used -  Implicit differentiation -     It is a rule by which we can find the derivative…