(a) | T(2x – x²) dx

Q: xcosx Q2- Find for y dx x2+4

A: We use logarithmic differentiation

Q: d -(3x² + 11)e¬ª at x = –1. dx Evaluate

A:

Q: Find the value of df/dx at x= f(a). f(x) = x² - 2x+ 4; a = 3

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Q: Find for the following functions: - dx 3x2-4x+4 1) y = %3| Z

A: dydx is called the derivative of function y.Derivatives of polynomials are :→dxndx =…

Q: Find d'yldx implicitly in terms of x and y. x²y = 4x = 6 dx2

A:

Q: Find the I.F of dy/dx= 1/(2xy)

A: Given that, dydx=12xy we have to solve this differential equation.

Q: Let y3 - 4x = 2xy. Find d2y/dx2. Show work please.

A:

Q: Determine dy for y=VX2+1 . dx2 alx

A: Obtain the second derivative as follows.

Q: 4 dx. x'V16-x (c) By using x= 4sin (0), find

A: We have to find integration by substitution

Q: +y = e* + cosh 2x+x +y%3D

A: Solution:-As per guidelines I submit first question only

Q: Find for all of : dx 1- y = xvInx x(x-2) x²+1 2- y =

A:

Q: J; x² x² - 1 4 dx

A:

Q: What is f P-(x)dx if the given DE is y(6y2 – x - 1)dx + 2xdy = 0?

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Q: ential equati x²y dy = C

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Q: d²y nd by implicit differentiation if 3x² – 7y? = 14. dx?

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Q: (x+1 0SxS2 f(x) = { Then what is the result of| ($2) dz 5

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Q: 3 Evaluate: ³₁²₁ ¹²[z³(x + y)³] dz dy dx -4 1

A: Given

Q: (f) / x² + 4 dx

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Q: y +6 dy (Int. of Rational func.) y? + y` 2)

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Q: Find dy. y = x| 13 dy = (Simplify your ans × |5

A:

Q: dx V2x-x2 /2х-х2

A: Evaluate ∫42x-x2 dx

Q: O g(x) = (3t+ 2) dl t %3D

A:

Q: Differentiate the function. y = (3x- 1)* (4 - x5) 3 dy dx II

A: To differentiate the given function:

Q: d²y Find for the following function. 2 dx y= (3x² +1) -5 d²y dx² =

A: Given: y=3x2+1-5 To find: the second derivative of y. The power rule of differentiation states that…

Q: If fe F dr = Sc(x - 2y³) dx + (x²y) dy, what is F?

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Q: So lve the Rollowing (x" +2y") dx %3D

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Q: find the dy さ× when 3In X リ=(メ+z)m

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Q: dy Find for y = x(4x + 3) dx - |3

A: The function is given by y = x4x+313 To evaluate : dydx

Q: x +2 . Determine the value of dx using method of substitution 1x* +4x+7

A:

Q: For the function y = f(x) - 4x 10: = | df at x = – 1. dx - 1. a. Find f'(– 1) =

A: SOLUTION-

Q: dx Evaluate V- x² – 4x – 1

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Q: - Trig Sub 1 dx V9 – x²

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Q: dx メ+Vaxt) dx |-x2

A: Given

Q: dy for all of : dx Find 3 |x(х-2) 1- y = xvlnx 2- у 3 х2+1

A:

Q: dy Find of y = e4-3x + 63x*-2 x+5 dx

A: Given  y=e4-3x+63x4-2x+5 Find dydx

Q: J 2x - 11 dx 2 x²+x-6

A:

Q: If F(x) 2 3x3 is an antiderivative of f(x), find / (-3f(x) – 4x³) dx.

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Q: (b) Given that, V2x + 1 and y = 1, when x = 12. Express y in terms of x. %3D dx

A: Topic :- Differential equation

Q: Evaluate [(x² +2) dx , using Trapezoidal rule, by taking N = 8.

A:

Q: Evaluate. (Use C for the constant of integration.) x3 + 25 dx x2 + 25

A: Given that: ∫x3+25x2+25dx

Q: Find the antiderivate of dx/(x2+4)3/2

A:

Q: Find the antiderivative of the function 4x3 - 2x2 +x - 5 dx

A: This question is based on indefinite integral.

Q: x2 — х + 36 dx х3 + 6х

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Q: For y = 5x2 + 10x - 3, find dy at x 4 if dx 0. 1.

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Q: Find for the following function: dx 4- y = In2 5- tan-1 V4x - 5

A: Topic : differentiation

Q: Let ƒ(x) = x2 - 4x - 5, x> 2. Find the value of dƒ -1/dx at thepoint x = 0 = ƒ(5).

A:

Q: 41 Cx) = 7x² +Y all fla) = bl flath= a fla la) - thl-f

A: Given function is:                                 (1) a) To evaluate Substitute  in equation (1)

Q: 3 Differentiate the expression (x + y )" with respect to x. (Use D for 2). dx

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.