Given f(g(x)) = cos²x what is the outside function f (x) and the inside function ? g(x) so that the Chain Rule can be applied to differentiate f(g(x)) f (x) = cos x, g(x) = x² All of these will work f(x) = (cos x)², g(x) = x f(x)=x², g(x) = cos x f(x) = (cos x)², g(x) = cos x

Q: Given that f(x) = V h(x) = x³ g(x) = = %3! Find (f ogo h)(x)

A: Composite functions concept is used.

Q: find the function f(x) if f'(x)=(2/1+x2)+(5/7)x5/7 and f(0)=2

A: Given, f'(x)=(2/(1+x2))+(5/7)x5/7

Q: Let F(x) = f(x¹) and G(x) = (ƒ(x))ª . You also know that a³ = 14, ƒ(a) = 3, ƒ'(a) = 12, ƒ' (aª) =…

A:

Q: Let ƒ (x) = x³ – 5x² – 8 and let g be the inverse of f (i.e. g (x) = f -1 (x).

A:

Q: Calculate the derivative of the function. f(x) = [(2x – 1)2 + (1 – x)°]? %3D f'(x) = %D

A: We will find the derivative using chain rule.

Q: nd and simplify 2² x² (f(x) g(x)). O d² O −(ƒ (x) g(x)) = ƒ” (x) g(x)+ f (x) g″ (x) Hint 2² -(f(x)…

A: Given query is to find the double derivative.

Q: Let F(x) = f(f(x)) and G(x) = (F(x)). You also know that f(8) = 6, f(6) = 3, f'(6) = 14, f'(8) = 3…

A: F(x) = f(f(x))F'(x) = dF(x)dx = df(f(x))dxF'(x) = f'(f(x))f'(x)F'(8)=f'(f(8))f'(8)        =…

Q: Find f'(x) and simplify. f(x)= x x+2 Which of the following shows the correct application of the…

A: F′(x)=(x+2)22​Explanation:If you have any questions let me know in comment box thankyou for your…

Q: f(x) = In(5 + 4x)

A: Given: - The function is, f(x)=ln(5+4x) To find: - The derivative of the given function.

Q: Let h(x) f(æ) If f(x) = 3 cos (x) and g(x) = 3x + 2x2 – x + 4, what is h' (x)? (æ)6

A: Given: f(x)=3cos(x)g(x)=3x3+2x2-x+4   Let h(x)=f(x)g(x).   Then, h(x)=f(x)g(x)=3cos(x)3x3+2x2-x+4

Q: Verify that f′(x) = g′(x) and explain the relationship between f and g

A: fx=3xx+2f'x=ddx3xx+2=x+2(3)-(3x)(1)x+22=3x+6-3xx+22=6x+22

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(4) = 11, f(11) = 3, f'(11) = 8, f'(4) =…

A:

Q: Find f if f"(x) = 2+ cos(x), f(0) = 2, f(t/2) = -2.

A:

Q: Let F(x) = f(f(æ)) and G(x) = (F(x))² . You also know that f(3) = 6, f(6) = 2, f'(6) = 5, f'(3) = 15…

A:

Q: I don't really understand the question below Given f(x) with f(1) = 2 and f′(1) = 5, find (a):…

A:

Q: If f(x) = cos(2x), then f"|

A:

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

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(3) = 9, f(9) = 3, f'(9) = 12, f'(3) = 5…

A: Given functions are Fx=ffx and Gx=Fx2. Also we have given f3=9,f9=3, f'9=12, f'3=5 Differentiating…

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that aª Then F'(a): = = = 8, f(a) = 2, ƒ'(a) =…

A:

Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: f(x) = x' +x² +1 and g(x) = 4 – x²

A:

Q: Find F'(x), f"(x) and f'"(x) for f(x)=x$+cos(9x).

A:

Q: Find f if f" (x) = 2 + cos(x), f(0) = -8, f(T/2) = 8. *(x) :

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that f(9) = 13, f(13) = 3, f'(13)=9, f'(9) = 7…

A:

Q: Let f'(x)= = (x-1) (x-2)(x+1) and g'(x) = (x+2)(x-3) (x+3)

A: We have to find the interval in which f(x) and g(x) are decreasing.

Q: = (F(x)). Let F(x) = f(f(x)) and G(x) You also know that f(3) = 12, f(12) = 3, f'(12) = 7, f'(3) =…

A:

Q: f(5)(x)

A:

Q: ng the table below. 3 4 3 1 4 3 3 2 1 2

A: We have to find the value of the given following conditions according to the given information