If F(x) = f(g(x)), where f( – 4) = 9, f'(– 4) = 6, ƒ' (2) = 1, g(2) = – 4, and g'(2) = 8, find F'(2). F'(2) %3D

Q: If f' (4) = -9 and g ' (4) = -5, find (a) h'(4), if h(x) = 10f(x) + 2. %3D h'(4) = %3D (b) F'(4), if…

A: Recall: (αf(x)±βg(x))' = α f'(x)±β g'(x) ; where α and β are real numbers.

Q: If f(x) + x2[f(x)]ª = 18 and f(1) = 2, find f '(1). %3D f '(1) =

A:

Q: If F(x) = f(g(x)), where f(-2) = 3, f '(-2) = 5, f '(-4) = 4, g(-4)= -2, and g'(-4)= 3, find F…

A:

Q: Given f(x) = In(- 4e" – 13), f'(x) = %3D

A:

Q: (2-9x³), find f'(x). Given f(x)= In (2-9x³), f'(x) =

A:

Q: Given f"(x) = 6x - 1 and f'(-3) = -3 and f(-3) = -4 Find f'(x) =  and find f(1)=

A: Given f''x = 6x-1    and f'-3 =-3                                  f-3=-4Now  We know f'x = ∫f''xdx…

Q: If f(x) = 5x¹(²), find ƒ'(6) to 3 decimal places.

A: The given function,   f(x)=5xlnx

Q: (D) h(x) = 12g(x) – 11f(x). | h'(2) = (E) h(x) = 10f(x) + 9g(x) – 2. %3D h'(2) = (F) h(x) = –10g(x)…

A: Given that :- f'2=-6g'2=9h'2=?

Q: If f and g are functions that satisfy f'(2) = -3 and g'(2) = -1, find h'(2) for h(x) = -5f(x) +…

A:

Q: Given f''(x) = 4x – 5 and f'( – 3) = 3 and f( – 3) = 6. %3D Find f'(x) = and find f(3)

A: Given, f''x=4x-5 , f'-3=3 and f-3=6 We have to find f'x and f3.

Q: Given f''(x) = 4x – 6 and f'( – 1) = – 2 and f( – 1) = 4. Find f'(x) = and find f(2)

A:

Q: If f is the function f (x) = + 4/x, then f' (4)

A: The function is  f(x)=4x+4x

Q: If f and g are functions that satisfy f'(2) = 5 and g'(2) = −2, find h'(2) for h(x) = 2f(x) - g(x) +…

A:

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

A:

Q: If f(x)= 4x+7/5x+2, find: f'(x)= f'(5)=

A: Given,         fx=4x+75x+2

Q: If f'(x) = 12r + 3z² and f(1) = 7, find f(x) . f(x) =

A:

Q: If f(x) = 3x – 3e", find: f'(x) = f'(3) = %3D

A:

Q: If f(x) = 7x² f'(2) = f''(x) = f''(2) = 8e, find:

A: The given function is fx=7x2-8ex

Q: g(x)= 2f(x) +3, find g'(4) given that f'(4)=5.

A:

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

A:

Q: Given "(1) = 9x + 2 (1),.. and f'(0) = - 5 and f(0) = Find f'(x) = und find f(3) =

A:

Q: 3 If f(x) = (5x + 7) find f'(). %3D Find f'(1).

A:

Q: Given f''(x) = 3x + 3 and f'( – 3) = 4 and f( – 3) = 5. Find f'(x) = and find f(3)

A: NOTE: Refresh your page if you can't see any equations. . take integration  ...............(1)

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.