. Solve the following problem (a) Y'(t) = XY(t) + 1, (b) Y'(t) = \Y(t)+t, Y(0) = 1. Y(0) = 3.

Q: 5. Suppose f(g(x)) = 4x/(x+ 1), and that 8(1) = 2 g'(1) = 1/4 8(2) = 3 g'(2) = 1/6 8(3) = 4 g'(3) =…

A:

Q: 6. (1 + x)y' + y = √x

A:

Q: f(x) = 3x² - 2cos(x) find the equation for f'(x).

A: Consider the fucntion

Q: 4. Let f(x) = e3h(x) and g(x) = h(e3"). Find f'(7) and g'(2) given that h(7) = 2, h'(7) = 4, h'(e) =…

A: We have to find

Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

A:

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

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

Q: 3. Find g if g'(x) = 8x(x® – }) and g(2) = 3. %3D %3D

A: We will find g.

Q: 3- 2 -3 2 -1 2 3 g(x) = sinh(x) -1 -2

A: the symmetry used here is the y-axis which divides the graph into 2 equal portions.  the graph given…

Q: 3. Given f(4) = 1, f'(4) = 3, g(4) = -2, g'(4) = -5. %3D %3D If h(x) (2x3+1)f (x) Vxg(x) calculate…

A: Given that, hx=2x3+1fxxgx Differentiating with respect to x we get,…

Q: 2 (c) f(x) = Find f'(4). 后

A: Given that the function fx=2x

Q: If ƒ(4) = 3 and fƒ'(4) = −5, find g'(4) where g(x) = √xƒ(x).

A: To find g'(4) where g(x) = sqrt(x).f(x)  also given f(4)=3 and f'(4)=-5Derivative using product rule…

Q: sec? =(3),4 = 2~/2+3, find h(1). 4 If k'(t) = sect+cost and if %3D

A:

Q: dfy = 12 - 30x, y'(0) = 7, and y(0) = 2. dx2 Find the function y(x) satisfying = 12 - 30x, y'(0) =…

A: Given:

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 = ƒ'(2) = g'(2)…

A:

Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

A:

Q: Given the graph of y = g(x), estimate the value of g'(2). (a) -4 (b) -1 (c) 0 (d) 1 $10 3 (c) 4

A:

Q: 6 3 Find h'(t) if h(t) = 5/6 ¯ ,1/5

A:

Q: Siven that y = f(x) passes through (2, 1) and f'(x) = 3x² - 5x, find f(x). %3D

A: Given query is to find the function

Q: 12 If f(t) = find f'(t). f'(t) =

A:

Q: 4. Find the second derivative for the following function a) )* 22 y3(x+ (an b) f(x)=/2x + at x= 2 c)…

A: See the attachment

Q: 12.Find the derivative of f(x) = x²e2x-6 at x = 3. (A)–16 (B) -12 (С) —18 (D) 20 (E) 24

A: Given : f(x) =x2e2x-6

Q: 1. Find f(x) if f'(x) = x/x and f(1) = 2

A: Given that: f'(x)=xx and f(1)=2

Q: 13. The graph of y = f(x) and y = g(x) are shown below. g(x) 6 (a) (b) f(x) 2 10 -2 Find h'(9) if…

A: Explained below

Q: 1. If h(x) = (f(x))² – (g(x))² , f' (x) = -g(x) and g' (x) = f(x), then h'(x) = (a) 0 (b) –4f(x).…

A:

Q: 8. Consider the function f(x) =6x5(x6+10)4 (a) Define u(x) = x6 + 10. Then calculate: u'(x) = (b)…

A:

Q: 1. f(x) = 6x + 15 find f'(x) Answer:

A:

Q: Use p(x) = In(x² + x + 7) to answer the questions below. (a) Find p'(x) = (b) Find the equation of…

A:

Q: 2. Differentiate the following equations. a. b. C. d. 9. h. f'(x) = f'(t) = f'(x)= F'(t) = A'(s) =…

A:

Q: Find y as a function of x if y(0)=29, y'(0) = 16, y"(0) = 20. y(x)= = y" — 11y" + 18y' = 32e,

A: