dy Find the function y(x) satisfying = 30, y'"(0) = 4, y'(0) = 6, and y(0) = 6. 3 d'y = 30, y''(0) = 4, y'(0) = 6, and y(0) = 6 is. The function y(x) satisfying %3D dx3

Q: Dy/dx=(3x-5)(x+1);y=1 when x=-1

A: Given equation is: dydx=3x-5x+1 And the condition is: y=1 when x=-1

Q: 1.2 s Find first derivative for the following functions. dx (a) y = 5+ 6x + 4x3 (b) y = In(2x) +x*…

A: Note:-Since you have asked multiple questions, we will solve the first question with three sub-parts…

Q: (1+x*)dy + x(1+ 4y²)dx =0

A:

Q: (xy² + x)dx-(x²y-y)dy = 0, y(2) = 5.

A:

Q: (B)(10M) Evaluate (y(x)) dx y(x) = cot (csc(sec(In x))) %3D

A: derivative

Q: 3x(xy - 2)dx + (x³ + 2y)dy = 0; f(1)=2 Find the positive root of y at x=2. Use 2 decimal places.

A:

Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: -g(x) = x²sinx cosx . Find g'(x).

A: We will use the product rule of differentiation to find the derivative.

Q: y=u (1+u³)* and u = (3x - 2)²

A:

Q: f'(x) = 6Vx ; f(1) = 7,

A:

Q: If a function y = f(x) satisfies = y, %3D then %3D dr y = e".

A:

Q: Find y as a function of t if 25y"- 70y' + 53y = 0, and y(5) = 8, y'(5) = 1. %3D y = %3D

A: Given: 25y''-70y'+53y=0  with the IVP y(5)=8 ,    and   y'(5)=1By…

Q: (a) Define what it means by for y = f(x). %3D

A: In this question we have to define the meaning of dydx for y=fx

Q: S (8)0.5x dx 2

A: Consider the integral as, I=∫2480.5xdx Simplify the expression as,…

Q: ((x + 1)5 + 3y)dx − (x + 1)dy = 0

A:

Q: 9. [f(x)dx -1

A: Find the integral from the given graph

Q: 1 dx (b)

A: Given interval :

Q: Find f such that f'(x) = 4x – 3, f(4) = 0. %3D %3D f(x) = D %3D

A: Given that: f'(x)=4x-3, f(4)=0

Q: Find f. (x + 1) f'(x) = (1) = 3 %3D f(x) =

A:

Q: Let P(x) = F(x)G(x) and Q(x) , where F and G are the functions whose graphs are shown. G(x)' F 4 2 G…

A:

Q: (dy/dx)-(x+3y)/(2x)=0

A:

Q: 4 xf (x* )dxif f(x)dx = 5. Find Enter the exact answer. f (x* )dx=

A: given:-∫04f(x)dx=5now∫-20xf(x2)dxlet,x2=t2xdx=dtxdx=12dtx=-2,    t=4x=0 ,       t=0

Q: Find the derivative of y = f(r) = VI(3r + ²). x(3x+x %3D

A:

Q: The profit function (in dollars) for a product is given by P(x) = 8x° – 0.25x + 1000, 0 <x< 24. Find…

A: The profit function is given as Px=8x3-0.25x4+1000, where 0&lt;x&lt;24. Obtain the first derivative…

Q: Let f(x) = 9 + V2x - 9. Find f(r).

A:

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:…