Find the general solutions for the following ODEs for a certain y(0) and y'(0)

Q: If a(x) = 2 – 8x, what is an equation for a (x)? O A. a-1(x) 2. 8. O B. a '(x) = ?= 2 8 al(z) = ", 으…

A: The given equation for a(x) is: a(x)=2-8x

Q: You are given the following function. 4t G(t) t + 9 (a) Find the derivative of the function using…

A: We will use the quotient rule of differentiation to find the derivative of g. While finding domain…

Q: Find the derivative. 5 (2x-3)* f(x)=- OA f(x)=- <-40 (2x-3)³ O c. f(x) = OB. f(x)=- OD. f(x) = 5…

A:

Q: g(x) = h * * A Xo elka

A: We know that: a·f'=a·f 'f·g'=f '·g+f·g'   Here, a is a constant.

Q: You are given the following function. 10t G(t) = t + 7 (a) Find the derivative of the function using…

A: The objective is to find the derivative of the function using definition and find domain of G(t) and…

Q: 2. Find the derivative of each of the following functions: y = x¹2 (i) (ii) (iii) (iv) y = 3x ¹ y =…

A: 1) y=x12Differentiate w.r.t.'x'dydx=ddx(x12)We know thatddx(xn)=nxn-1Thereforedydx=12x11

Q: If f(x) = x' – 8x + 2, find f (-4).

A: We have,  fx=x3-8x+2           ⋯⋯1

Q: Calculate the derivative of the function. g(x) = (4a? + 2x +2)* O g' (x) = (-16æ² + 8x + 8) O 9' (x)…

A:

Q: 1. f(x)= xsin x 2. f(x) = x?cos 2 x 3. f(x) = tan x – sec x sin x 4. f(x) =

A:

Q: x + 2 Consider the function f(x) Compute each of the following. Simplify your answer and use exact х…

A:

Q: Find all possible functions with the given derivatives. a. y' = 2x b. y' = 2x - 5 c. y'= 3x² - 2x -…

A: a y'=2x           b y'=2x-5           c y'=3x2-2x-5

Q: The process of finding derivative is called a 4-step rule in which the steps are summarized as…

A:

Q: Find the derivative of the ff. 3. f(x)= +an (x²- 2x) 8.h(x) = (4) -* -x2

A: Using chain rule.

Q: X = 6. (x)f (q (x 3. = (x)6 (3x 1. Determine the first derivative of the following functions:

A: