b\ State and prove the theorem of (derivative of inverse functions), then use it to answer these questions below, for each given functions find the value of f-¹(x) at the points that referred: dx (1) f(x) = logax, for all x (2) f(x) = ex + 2x + 1, at x = 2, iff-¹(2) = 0. (3) f(x) = 2x³ + 3x² + 7x + 4. at x = 4

Q: Let f(x) = *+3_ 2x + 1 a. Find a function formula for f-'(x), the inverse function of f. Show your…

A: For inverse function put f(x)= y and find x in terms of y , that will be inverse of f(x) , now  For…

Q: Use logarithmic differentiation to expand and differentiate y =(x+4)8 / sqrt x4+9

A: we have given y=x+48x4+9now apply log both sides ,we getlog y=logx+48x4+9=8log(x+4)-12log(x4+9)now…

Q: Given the function, find the derivative f (x) = -()" 3z 4 3z- 3 12() 3z-4 O None of the Above

A:

Q: Can you use logarithmic differentiation to find the derivative of function

A: Step 1:

Q: Given functions f and g for which f(- 6) = 1, ƒ'( – 6) = 1, g( – 6) = 6, and g'(- 6) = 2. Evaluate…

A:

Q: Find each derivative 4) y = x-* (use logarithmic differentiation)

A:

Q: g(x)=√3-x State the domain for the function and it's derivative using interview notation

A: We have to find the domain for the given function and it's derivative

Q: Use logarithmc differentiation or lanofher method to, find then derivative

A: The function is given by fx = x2x, x>0                                    ......1 To evaluate:…

Q: 3x' +2Vx For the function F(x)= find the first derivative and simplify.

A:

Q: y = ln(5t³ - 6) y = ln(4- 3x²)

A: y=ln⁡(5t3−6)

Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

A:

Q: Consider the following function: f(x) = 2 8 - 9 - Step 1 of 4: Determine f'(x) and f "(x).

A: on differentiation we get