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: Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) > 0 and f"(x) <…

A:

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

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

Q: If f(x) = 3x³ - 6e*, find: f'(x) = ƒ' (3) = ƒ''(x) = = f''(3) =

A: Given, f(x)=3x3-6ex

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

A:

Q: Let f and g be the functions in the table below. N X f(x) g(x) f'(x) g'(x) 1 3 2 4 6 2 1 3 5 7 3 2 1…

A: (a)Consider, F(x)=f(f(x))Differentiate with respect to x. (Use chain rule of…

Q: Let F(x) = f(r°) and G(r) = (f(x))° . You also know that a = 12, f(a) = 2, ƒ'(a) = 15, f'(aº) = 5…

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x   Given: Fx=fx9 ;…

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 ƒ(8) = 11, ƒ(11) = 2, ƒ'(11) = 5, ƒ'(8) =…

A:

Q: Let f(x) = x' - 3x° + 2x- 2x 5. %3D Then f'(x) is f'(4) is f"(x) is and f''(4) is

A:

Q: If find f'(x). ƒ'(x) = | Find f'(4). ƒ'(4) = f(x) = = 7-x² 8+x²

A:

Q: g(x)=2x-1

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

A: We can solve as follows Do not confuse in round bracket and close bracket. They are same in this…

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) = 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: 7 + Vx + x dx

A:

Q: Find h(x) if h'(x)= h(x): 5x (6-x²)² X and h(1) = -6.

A: NOTE: Refresh your page if you can't see any equations. . here we have take integration on both…

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: If f, g, and h are f A(x) = (xf)' (x²f)" A'(x) = f f' (x³f")" differentiable 8 (xg)' (x²g)"…

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

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…