8. Which of the following statement is true? ○If h(x) = f(x)g(x), then h'(x) = f'(x)g'(x) f(x) = g(x), OIf h(x) f'(x) g'(x) ○If h(x) = f(x)g(x), then h'(x) = g'(x)ƒ(x) + f'(x)g(x) f(x) then h'(x) = g'(x)ƒ(x)+ƒ'(x)g(x) OIf h(x)= = g(x)' g(x)² ONone of these. then h'(x) = =

Q: Let f(x) = (x³ + 3x + 7)3 f'(x) = f'(4) =

A: According to question given thatf(x)=(x3+3x+7)3

Q: Suppose k(x) = f(g(h(x))). Given the table of values below, determine (-1). f(x) g(x) | h(x) | f'(x)…

A: We have to find derivative

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: f'(x) = +6) ¹¹(™). Find f'(x). Let f(x) = (x³ + 6)¹(x).

A:

Q: Consider the function. f(x) = x R(x) + Q(x) Identify the derivative f'(x). f'(x) = xR'(x) + R(x) +…

A:

Q: If f(x) = f' (x) for all æ, then f(x) = = f" (x) for all x. True False

A: f(x) = f'(x) for all x Then f(x) = f"(x)  for all x

Q: (-7)=|

A: Topic:- derivatives

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(5) = 6, ƒ(6) = 2, ƒ'(6) = 6, ƒ'(5) = 12…

A:

Q: -7 Let f(x) 7xVI + f'(x)

A:

Q: can you explain if this statement is true or false if h(x)=f(g(x)), then h'(x)=f'(g'(x))

A:

Q: X x+18

A: f(x)=xx+18

Q: Find a function f(x) such that f'(x) = 9x² +2 and f(0) = 1 f(x) =

A:

Q: and g(x) are differentiable functions, suppose that f(-2) = 1; f(1) = 5; f'(-2) = 3; f'(1) = 3;…

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that ƒ(8) = 11, ƒ(11) = 2, ƒ'(11) = 5, ƒ'(8) =…

A:

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: ax², x 2 then f(0) = 0 If f (x) = lx² + b, x > 2

A:

Q: Let F(x) = f(x) and G(x) = (f(x))*. You also know that a³ = 12, ƒ(a) = 3, ƒ'(a) = 5, ƒ' (aº) = 8…

A: If we consider a function y which is a function of x only. Then, the derivative of y with respect to…

Q: Let F(x) = f(x) and G(x) = (f(x))³. You also know that a = 3, ƒ(a) = 3, ƒ'(a) = 11, f'(a³) = 9 Then…

A:

Q: Let f(x) = 5x² cos(2x). f'(x) = -10x²(2x) + 10x cos(2x) f'(5) = 0 f"(x) = -10x² sin (2x) + 10x…

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: Suppose f(æ) = |x| · x Then f-l(x) = if æ > 0, and f-'(x) = if x < 0.

A: given that fx= x.xfind f-1x for x≥0 and x≤0

Q: Suppose k(2) = f(g(h(x)). Given the table of values below, determine k(-2). f(x) g(x) | h(x) | f'(x)…

A:

Q: Suppose that Find f'(2). f'(2) = f(x) = = e³x x² + 4

A: Given f(x)=e3xx2+4   We are required to findf'(2)         The following formulas of derivatives has…

Q: What conclusion can you draw if f' (c) = 0 and f'' (c) &lt; 0?

A: Given: f' (c) = 0 and f'' (c) &lt; 0

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

Q: Let 4 f(x) = (x³ + 2x + 5)* f'(x) = f'(4) =

A: Given: fx=x3+2x+54 Now to find the derivative of the given function, By using the chain rule for the…

Q: Let F(x) = f(x³) and G(x) = (ƒ(x))⁹. You also know that a8 = 15, f(a) = 3, f'(a) = 10, ƒ'(aº) = 12…

A: Firstly we differenciate the given function and then put given values.