(c) [ n@dx In(x) dx x2

Q: Зx + log dy find dx If y = 4 — Зх -

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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: Find a function of the differential equation: y = x²-2 sin x

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Q: Solve the differential equation – xtan(y – x) = 1 dx

A: Using substitution y-x=t We can reduce inform of variable separable

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

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Q: In (3x) Find the derivative of y with respect to x if y= sin (7 e') dt. dy dx

A: Given : A function is given as: y=∫0ln3xsin7etdt To find : The derivative of the function y.…

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

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.33).

A: The linear approximation of f(x) at x=a is given by L(x)=f(a)+f'(a)(x−a) Given, f(x)=ln(x) at x=1.…

Q: 10. Find the derivative of y = ln 4**+1) In 4 dy A) dx 2x dy 2x In 4 B) dx dy 2xIn 4 C) dx 4(*+1) dy…

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Q: find dy dx 15 In 4+ xe) 6

A: dlnax+bdx = a.1ax+b.

Q: dy (sec x) dx eуtsin x

A: Given : The differential equation sec xdydx = ey + sin x

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: 3x =2 when x= What is the particular solution to the given differential equa

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Q: Find dy/dx of e*-e-x y = e*+e-*

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Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: (a) Find the derivative. = In(x) – In(x - 8) dy dx (b) Find the derivative. y = In X - 8 dy dx %3D

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Q: the chain rule - find dy/dx (derivative) of y= (4x11 + sin(5x))1/8

A: We have been given a composite and complex function, and we are required to find its derivative. In…

Q: Find dy dx I-Ln(x+3)=tかが(x:)

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Q: Solve the differential equation: (2xy-sinx)dx+(x² - cosy)dy=0.

A: The given differential equation is  (2xy-sinx)dx+(x2-cosy)dy=0 It is of the form , Mdx+Ndy=0 . This…

Q: 53. df = (x+ 1)ye"dx + xe*dy

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Q: a) In(x+1)³ dx x+1

A: Given, ∫23ln(x+1)3x+1 dx

Q: -32e* – 140 -dx J e2x +9e* + 20

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Solve the differential equation by variation of parameters. ✓+y=sin²(x) - con(x) + cylin(x) + con(x)…

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Q: y = (cos x-x4+ 1/x2)5 - In (3x+1)  Find dy/dx

A: =?

Q: A-The derivative is y = In sin 0 cos 0 1+2 ln 0

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Q: Find the differential equation corresponding to y=a cos (logx) +b sin(log x)

A: Chain rule of differentiation: [f(g(x))]'=f'(g(x))g'(x) Formulae used: ddxcos x=-sin xddxsin x=cos…

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

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Q: (a) Find thne derivative. y = In(4x – 6) – 3 In(x) dy dx

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

Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: Find a function of the differential equation: y' = x3-2 sin x

A: topic - differential equations

Q: ¹In(1+x) -dx X

A: According to guidelines we must answer only one of the multiple questions given. So, I answer only…

Q: - Find dy/dx for y = log2(1 – sin³ (3x²) %3D

A: Use the chain rule to differentiate the given function.

Q: Solve the differential equation tan x- dy ey-cotx dx

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Q: Solve for the differential equation: dy/dx - ytan x = cos x

A: To find the solution of the linear differential equation of first order y'+Py=Q, where P and Q are…

Q: – (x²- 1) dx using P (1 -;*)-^;* / * m in terms of A?

A: Use simple integration formula.

Q: How would I Find dy/dx implicitly 5xy + ln(x2y) = 9

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Q: Solve the ordinary differential equation (ODE) dxdt=5x−3 for x(t).

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Q: Demonstrate that the function f(x)= e^-x sin (x) is a solution for the differential equation f(x) +…

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Q: 3- Coshx dy +ly sinh x +e) dx

A: We have to find the solution of differential equation

Q: 1 B3. Evaluate dx, using substitution method.

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Q: dy Find dx by logarithmic differentiation. e2x – 1 y = In e2x + 1

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Q: Solve for the differential of y when y- sinax. x= and dx O o o

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Q: Consider a differential equation y' = xy + xe -x

A: To solve a differential equation:

Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 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: - if eV = In(x) + In(y) + e³ ху 3 Find dx

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Q: (1) | cosx In (sin x) dx (2) [ xe -TX | хе dx x (3) x -16 dx

A: As per guidelines, we are supposed to solve only first two questions. Please repost other questions…

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

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Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.