1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3.

Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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Q: Solve the first derivative of f(x) = e-2x In x at x 0.5 using forward finite-divided difference and…

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

Q: Find y" by implicit differentiation. x² + 5y2 = 5 %3D

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Q: Find the differential of the function: y = x In x

A: Solution:Giveny=x ln xTo find the diffferentiationformula:(uv)'=uv'+vu'ddxxn=nxn-1ddxln x=1x

Q: In xy = x² + sin xy

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Q: find (y') by Implicit differentiation e(2x+3y) = x² – In(xy³) 1 Add file

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Q: find the derivative of y with respect to x, t, orθ, as appropriate.

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Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: Find y" by implicit differentiation. x² + 4y² = 4

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Q: What is the average rate of change of y = cos (2x) on the interval [0,π/2]

A: Given f(x)= y=cos (2x) to find the average rate of change over the interval (0,pi/2) average rate of…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = In(cos(In 0)) %3D

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Q: Use implicit differentiation to find y' at (2, 0) for 2x2 + e2ay

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Q: In the integration What is the implicit derivative of u? V9-4x² a. du = 2dx %3D b. du = * c. du =-…

A: dx9-4x2=dx32-2x2 Put, u=2x⇒dudx=21⇒du=2 dx

Q: find the partial derivative of the function with respectto each variable. ƒ(x, y) = 1/2 ln (x2 + y2)…

A: The given function is fx,y=12lnx2+y2+tan-1yx.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: Find the derivative of function.

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Q: Find by implicit differentiation for x2+y2=25 at point P(0,5).

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Q: Evaluate the derivative of the function. y%3Dsec(6 In 8x) -1(6 In 8x) dy %D dx

A: The objective is to find the derivative of given function

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

Q: Find the derivative of y with respect to x. y = 5x4 sin-1 r 1 V1-x? + 20x3 5x4 1+x2 + 20x³ sin¬1 x…

A: We have to find the derivative.

Q: Find the total derivative of V with respect to X

A: As the differentiation is with respect to x, x becomes the variable. y and z becomes constants

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: Use implicit differentiation to find y′ and evaluate y′ at ​(−2​,1​). x ln y+4y=3x3

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Q: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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Q: the derivative of y with respect to v. 1 = In ( cosh (5v)) –· tanh 2(5v) 2 derivative of y with…

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Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: = Determine the equation of the tangent line to the graph of f(x) = I x+ln x cosh (√2t - 1) dt at x…

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Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

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Q: Find the differential of the function. u = 2x +

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Q: Consider the implicitly defined curve x²y = 3y + x + 3. Use Implicit Differentiation to find dy

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Q: Find y' in the function In (xy + x+ y) = 2 using implicit differentiation.

A: The given equation is: ln (xy+x+y)=2...(1)

Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: In the integration What is the implicit derivative of u? V9-4x* a. du = 2dx b. du = * c. du =– 2dx…

A: Implicit differentiation of integral

Q: Find the second derivative y “ of " of y = 5z +sin zcosz

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Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: C) use implicit nind ay differentiation to dn for 22 (Osh (y) - In (tanh 2) = y2 %3D

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Q: Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step…

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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: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…

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Q: ind the derivative of y with respect to x. y =-cos-16x + 7° 6 6. 1 + (6x + 7)2 81 - (6x + 7)2 O 4.…

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Q: Q Find the derivative us ing the de fini tion 2. O fcx) Fcx) x+2X %3D

A: Derivative of the function using definition

Q: Find the derivative of y with respect to x. 1 y = In x/x+5 dy dx II

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Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: 1. Find the derivative of g(x): Int dt 1+t Cos

A: This will solve by Leibnitz theorem

Q: Find the values of x on [0, 2 ) π where the tangent line of f x( ) be horizontal. y=e^-x (cosx)

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Q: 5. Find by implicit differentiation for x + y = xy. dx

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Q: V=ln( cosn 92) %3D

A: