A three times differentiable function fwith f'(x) 0 has a D-derivative at x given 2 f'"(x) 3(f"(x) Df(x)=(x) 2 f(x), 1. Compute Df(x) where f(x) = ex. 2 2. Show that D(f o g)(x) ((Df) g)(x) (g'(x))Dg(x) - Assuming that both Df(x) and Df-1(x) exist, find a formula for Df-1(x) 3. X tnt dt for t > 0. 4. Compute Df-1 (0) where f(x) = 1

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

A:

Q: If f is a differentiable function, then False True d da 1 = f'(x) f(x)²

A:

Q: If f(t) = (2t - ), find ƒ' (t).

A:

Q: Let f(x) = (x² + 4x) (x³ + 6) . Find ƒ'(1). (Hint: First take the derivative to find f'(x). Then…

A:

Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

A:

Q: f(x) = (2x – 3)²

A:

Q: Find the derivative of the function 3 f(x) = V (x² – 2)' at x = -1. f'(- 1) =

A:

Q: Find f'(a). 1 f(t) t2 + 5

A:

Q: Find the function such that f'(x)  = f(x) (1- f(x)) and  f(0)  = 1/2

A:

Q: y y=f'(x) 2

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: find f'(a) f(t) = 1/(t2+7)

A:

Q: Let f(x) - 6e* +2 + e'. f'(0) =

A: The given function is f(x)=-6ex+2+e1

Q: Let f(x) = 5 sec(5x) f'(x)

A:

Q: (

A:

Q: 1 Assume that f'(4) = -5, g'(2), g(2)=4, and y=f(g(x)). What is y' at x = 2? 8 Atx=2, y'= (Simplify…

A: The chain rule of differentiation is given by

Q: Find f if f"(x) = 0, f(0) = 2, f'(0) = 1

A:

Q: Find f'(x) and f'(c). Function Value of c f(x) = (x³ + 2x)(3x³ + 5x – 4) c = 0 f'(x) = f'(c) =

A: fx = x3 + 2x3x3 + 5x - 4fx = 3x6 + 11x4 - 4x3 + 10x2 - 8xDifferentiating with respect to x on both…

Q: If f(r) = 3 sec(8x), find f'(r)

A:

Q: Find f(x). f'''(x)=3sinx, f''(0)=3, f'(0)=1, f(0)=0

A:

Q: The first derivative of a continuous function y = f(x) is y' = x(x - 9)². Find y' and then use the…

A:

Q: If f(x) = (x+1)/(x-1), where x # 1, determine f '(1). %3D

A: derivative of fx=x+1x-1 at x=1

Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: Find f' in terms of g' if (i) f(x) = g(x + g(a)). %3D

A: We will use the formula f(g(x))' = f'(g(x))g'(x)