Let y(x) = > ana" denote the pe y'-y = x2, y(0) = 1. The val %3D

Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

A:

Q: store A's profit is modeled by f(x) = 3^x and store B profit is modeled by g(x) = 9x. Over what…

A: Please see the below picture for detailed solution.

Q: If h'(3) -1 and h'(1) = 5, then |h"(z)dr = %3D %3D (A) -6 (B) 4 (C) 5 (D) 6 (E) 9

A:

Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

A:

Q: if y= (1+e^x)X^3 then find y`

A:

Q: Help The number of mosquitoes in a lake area after an insecticide spraying decreases at a rate of…

A: Given,

Q: Determine the following value: F20 + F30 1. 2. F34 3. F67

A:

Q: y y' + (2х + 3у) = 0 y(x) = ? =>

A:

Q: sec?xsec'y dx dy .2

A:

Q: 2) y' – (cotx)y = -(2cosx)y2 %3D

A:

Q: Find y'  if e x/y      = x   -y

A:

Q: if y= 1/2x^3 then find y`(0.50)

A: We find y' or first derivative of y using power rule. d/dx(x^n)= n*x^(n-1)

Q: Let f(x) = x + 12 f-'(x) = %3D 1.

A: Let's say y = f(x) A function g is said to be inverse of a function f, if g(y) = f(x) Procedure to…

Q: Let 4 f(x) = (a + 4x + 4)* f'(x) = f'(5) =

A:

Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

Q: Answer y = ce-((lnx)^2)/2

A: Given differential equation is,

Q: y" - y' = -4 y(x) = %3D

A:

Q: e*(y' – y) = 2xy?

A: Given

Q: Let h(t) = 3t3.2 7t-3.2 %3D | Then h'(t) is h'(1) is s! (7),.4 and h''(1) is

A:

Q: -5 -4 -3 -2 -1 n y = دیار 2- 7 1 -2- -3- -4 2 3 4 10 5 Write an equation for the function graphed…

A: Given graph

Q: y-5y't 4y =O x10)-5 y'l0)=2

A: We have to find the particular solution of the initial value problem…

Q: 1 64 + 4f(1) + 7z²(f(x))* = 0 and f(1) = -2, find f'(1).

A: Given:

Q: Use the product rule to find the derivative. f(x) = (3x - 2)(6x + 1) %3D O f(x) = 36x - 4.5 !3! O…

A:

Q: Find g'(x) if g(x) %3D Зx е бх

A: Product rule of the derivative is, (uv)’=u’v+uv’ where u and v are the functions of x.

Q: What is the approximate value of the first derivative of S(x)=-0.1x*-0. 15x-0.5x-0.25x-1. 2 at…

A:

Q: f(x) = xV 3 - x² — х

A: Solution: The objective is to find the derivative of the given function

Q: y' = = x/n(x)

A: We can find the derivative of the given function by using logarithmic differentiation.

Q: Solve xdy = y(1+ ln y - In x)

A: We will solve the problem

Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: Find for implicit equation dx xy -e' = 3x*

A:

Q: - 1 Find y' for y = 7x-4 + 2x-1. y' =

A: We havey=7x−4+2x−1

Q: Estimate f'(5) of the function f (x)= 5ln(x). %3D O a. 1 O b. 0 О с. 5 O d. Ins 1 O e. In5

A: Given function is f(x) = 5ln(x) To find : f'(5)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.