Differentiate y' +y? - 5y - x? = -4

Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: z (y/)° = y

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Q: y = 2 ||

A: We have to find the derivative of the function y = 1-x2ex2

Q: Find the equation of the line normal to x3y-2xy2= - 4 at the point (-2,1)

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Q: Find the first four derivatives of y = 4sinx. %3D

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Q: Find y" by implicit differentiation. 3x3 + 4y3 = 2

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Q: X 1.-+ J y = 37ab2, y" X

A: Let's find.

Q: Parallel to x + 2y = 0; (1, 2) on line

A: To find the equation of line paralley to x+2y=0 and (1,2) is on the required line.

Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: 4 1 Y(s) = 5s2

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Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" :

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Q: y=C1x + C2e + x2

A: The givne equation is:y=C1x+C2e-x+x2To eliminate the arbitrary constant/s

Q: y = x* + 2 sin(x) + xº + 24*.

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Q: Differentiate: F(y) (y + 9y°) yA - y?

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Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" =

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Q: F(x) = -7+ x2 INTERUAL-ピ-3 -2. AUERAGE RATE of

A: Given query is to find the rate of change for the given interval.

Q: Find the slope of the line tangent to 2xy + π sin y = 2π through the point (1, π/2).

A: The slope of the line tangent to 2xy+πsin y=2π through the point 1,π2.

Q: Find the point on the line y=5x+3 that is closest to the origin (x,y)=(______)

A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: 3. = 2x-y х+3у

A: We will differentiate the given problem with respect to x.

Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: Find the Indicated Derivative dy 1. y = x5 - 3x* + 2x3 - 2x2 + 7x - 1, dx dy 2. y =x2+x-3 + 3, dx…

A: Given:- y = x5 -3x4 +2x3 -2x2 +7x-1 y =0.5x-2 + (2x-3/3) +3 To find:- dy/dx

Q: Determine the derivative of у. /20x+6 y = ev y =

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Q: 9. at the point (-2,1) Find the equation of the line tangent to y = 2x2 + 1

A: We will find the equation of the line tangent in the following step.

Q: Find anti derivative 3x^2(y^2+1)

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Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: How can you relate antiderivatives as an opposite of derivatives in your life?

A: Solution:   Antiderivatives are the inverse operations of derivatives or the backward operation…

Q: Find the slope of the line tangent to the graph of x2+2xy2+3y=31 at th epoint (2, -3)

A: To determine the slope of the tangent at the point (2, -3).

Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

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Q: Find y" by implicit differentiation. 4x3 + 5y3 = 6 У" :

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Q: Find the homogenous linear equation with real, constant coefficients that is satisfied by:…

A: Given that  Required differential equation is satisfied by   y= 6 + 3xe^x - cos x

Q: Find y" by implicit differentiation. 4x3 + 3y3 = 4 %3D

A: Given: 4x3+3y3 = 4 To find: The value of y'' by Implicit differentiation.

Q: Find the second derivative (y”) of 4x2 + 9y2 = 36 by implicit differentiation. a. -16y3/9      b.…

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Q: 4) Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5).

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Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: A) Differentiate y = 4Vx +- +1 8 6 B) Find the second derivative of y = 4Vx + 8 + 10 Vx

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Q: Find the derivative of 5e* 1. y = e 6x 3. y = 2x+3x 2. y = e* + e3x 4. y = (e* + ex)1/2

A: Quotient Rule of differentiation : ddxuv=v.dudx-dvdx.uv2 deaxdx=aeax dxndx=n.xn-1

Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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Q: ential equation is given by

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Q: 5z²)* 4/3 %3D

A: (3). The function is given by Hz = 1-5z243 To evaluate: The derivative of the function.

Q: Determine the second derivative of y = v5x² + 1 Determine the third derivative of y = (x² – 1) (2x3…

A: Second derivative of5x2+1 is  d2dx25x2+1

Q: What is the derivative of cy = 2 - a°y ?

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Q: Find y'' by implicit differentiation 4x3+3y3=6

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Q: y 1-

A: The solution is given below in the next step:

Q: 10.Anti-derivative of y(2y^2-3)^5

A:

Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

Q: Calculate the second and the third derivative of y = 5x- 9 y": y"

A: Using derivatives rule & formula.

Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

A: