If r(y) = e³y² +3 find r'(y) =

Q: Find y as a function of a if y(0)2, y'(0) = 3, "(0) = -13. y(x) = y″ − 4y″ − y′ + 4y = 0,

A: Given a differential equation:initial conditions are:

Q: If y = Vx? – 2x then y' 2(x-1) 3x2-2x %3D

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Q: y = V In(5x + 7)

A: In this question, we use the chain rule to find the derivative of the function .

Q: 3 3. y' for y² = x²y³

A: to find out the derivative

Q: Find y' and y". In(7x) y = x7 y' = y" %3D

A: The given function is: y=ln(7x)x7 Therefore, y'=1x7ddx(ln(7x))+ln(7x)ddx1x7    =1x717x·7+ln(7x)-7x8…

Q: Find y as a function of x if y(1) = 1, y'(1) = 4. y = x²y"-7xy' + 16y=x6,

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Q: Find y'. In(5x) y = 4x y' =

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Q: find y(x) for x2y'-2xy=3x with y(1)=3

A: Given,         x2y'-2xy=3x  with y(1)=3

Q: If R'(x)=250-18x and R(0)=0, find R(x)

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Q: Find y'. y = V In(7x + 5) y' =

A: Given the function y=ln(7x+5)         ........(1)

Q: Solve for y(x):  y’’ – 5y’ + 12y = 0; y(2) = 0; y’(2) = -4

A:

Q: If t²y" – ty – y = 0 ,y(1) = 3 and y'(1) = -1, then y(4) = . . . %3D

A: Given differential equation, t2y''-12ty'-y=0,y1=3,y'1=-1 Find the value of y4.

Q: Put the equation into the form x'(t) = g(t)h(x), and solve by the method of separation of variables.…

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Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: Find y' if y= y' = 4 x5 - 6x² +7 2 X

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Q: of y' = x²/(y + 1)?

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Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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Q: Find y' for y = 7x-3+ 5x - 1

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Q: Find y' if y = In(9x² + 5y²). y' = X

A: The given data is: y=ln(9x2+5y2)  Find y'

Q: Find y' if y= is-2x(+)* +

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Q: solve by bernoulli y' + (8/x)y = x6y4

A: We will find out the required general solution for given Bernoulli's equation.

Q: Find y' for y = 9x-6 + 7x¯1. y' =O

A: Given: y=9x-6+7x-1

Q: 9. Find y' if y – x²y = x³

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Q: y (2 xy +1)= xy'

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Q: 8) y'+y=17 sin(2t), y(0) =-1.

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Q: If g(x) = , what is g'(x)? 2x-1 x²+3x '

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Q: 3) Find y"(0), where y = 4x + 2x + 3

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: G(y) = (y − 1)4 / (y2 + 2y)7 Find G'(y) =

A: for a polynomial function of power n: Division rule of differentiation:         Chain rule :…

Q: (4) Find y' if y = xcot-12x -V1– 4x².

A:

Q: Find g'(4) given that ƒ(4) = 7, ƒ'(4) = −1, and g(x) = √xƒ(x). Answer:

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Q: Find y'. In(5x) y = 7x

A: SOME RESULTS:     IF y= f(u) and u=g(x) then,  dydx=dydududx.      ddxuv=vdudx-udvdxv2,v is non…

Q: Find y'(2)  y=ex2−ay=ex2−a where a=4

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Q: Find y' if y = 2vx (3x - 2) at x = 4. %3D

A: We need to find y' at x=4

Q: If y = (3x+8)x, compute y'(1). y'(1) = X

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The Product rule:…