[x* In(x? )dx = ?

Q: fr'e"dx 2-2 x

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Q: Find dy/dx of the following function

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Q: S.Si dx dy о 1+ху

A:

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: (8) dx Compared to I dx x In|x| Conterges or Diverges

A:

Q: the value of the integral dx 4.x(ln(9x))² 2

A: In the given question, the concept of integration is applied. Integration Integration is a method of…

Q: I = | In(ax + 1) dx, for a > 0

A: Find the integration of I

Q: dy y = In 1-х2 dx 1+ x2

A: To find: The derivative of y=ln1-x21+x2. Concept used: Chain rule of derivative: fgx'=f'gx·g'x The…

Q: 1 (In x+1)x dy dx

A: Given integral is evaluated as follows

Q: Use x = ey to explain why d/dx (ln x) = 1/x, for x > 0.

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Q: The derivative of the function y = sin-1(e* – In x), where Je – In x| < 1, is:

A: Recall ddx(sin-1(x))=11-x2 ddx(ex)=ex ddx(ln(x))=1x

Q: Find the indicated derivative. x2 dz for z = x? dx 1 - x - 5x dz dx

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Q: Find dy/dx by implicit differentiation for the following.:2y2 = 5 + x/5-x

A: Given: 2y2 = 5+x5-x Now differentiate the given function we get, By using the product rule,…

Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: Find the first derivative of the following functions with respect to x y = In(ln(In x))

A: To find first derivative of the given function.

Q: In(x) dx; u = In(x), dv = x³ dx

A: Use integration by parts method.

Q: Find dx by using logarithmic differentiation for = (Cos x)(e)

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Q: Given e^x - x^2 + y^3 = xy, find dx / dy using implicit differentiation

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Q: If X is an exponential RV with parameter A, find the PDF of Y = -14 In(X). 2

A: Given information: If X is an Exponential random variable with parameter λ. The pdf of X is,…

Q: Find the derivative. d 6. dx 6. X, dx

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Q: Find the derivative d/dx of the following 1 log sin(x)

A: We can find the derivative as below

Q: Use this information to evaluate 1 (1- e)| dx %3D x=1 et - 1

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Q: d² (¤Arctan x dx?

A: To find the following derivative of the given function.d2dx2x arctan x

Q: Find derivative /differential of each of the following functions by using the appropriate formula.…

A: y=x2 e2x  dy / dx  =?

Q: Find dy/dx of the following function. Implicit differentiation x3 + y3 = 8

A: Differentiation on both sides

Q: Does dy/dx= y-2y/x for ln(2xy)=x

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Q: Evaluate the function: S de x(x-2) -dx (x–1)³

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Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: find dy/dx for the given value of x.

A: Finding dy/dx

Q: 4 dx X-X-2Ą

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Q: dy for y =loge(l-Sin( 3x) Xア

A: We use chain rule to solve this differentiation

Q: a) In(x+1)³ dx x+1

A: Given, ∫23ln(x+1)3x+1 dx

Q: find the antiderivative of the following derivative  dy/dx= x^-2 e^-1/x

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Q: Integrate dx/(x+1)(x^2+16) from 0 to 1

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Q: Find (x' In(x)). dx

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Q: d y' of y= In(tanh2

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Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: Use the Simpson's rule to estimate e**dx with n = 4

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Q: -2(х-1 — х?) dx

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Q: Find the first derivative dy/dx of the following. Simplify. 1– x3 y = In 1+ x3

A: To Find the first derivative dydx of the function and simplify Given the function y = ln 1-x31+x3 y…

Q: Find the derivative of the function. sin(x) y = In(1 + 7v) dv g'(x) = Jcos(x)

A: Solution

Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

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Q: Find the derivative of y with respect to x. y = tan(In 4x) O A. x/1+ ( In 4x)2 1 О в. 1+ ( In 4x)2 4…

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Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: Sind dy forys(x) dx 3517X

A: y=(xx)3sin x

Q: Show that d/dx(ln kx) = d/dx(ln x), where x &gt; 0 and k is a positivereal number

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Q: Find the indicated derivative. dz if z = In (x° + e 5) dx dz dx

A: Given data is: z=lnx8+e5 To find the value of dzdx

Q: Find the derivative. d In dx ...... d dx

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Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

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Q: Find the length of the curve y = ln x from x = 1 to x = e.

A: Given:Find the length of the curve y = ln x from x = 1 to x = e.