2. Given that f is a differentiable function with f'(3) = -5, find g'(1) where g(x) = f(4x-x²)

Q: Given that h''(w) = - 34. State the function that best describes h'(w)

A: h"(w) = -34 Now to find h'(w)

Q: g(x) = 2x + 3 X - 5 Given the functions find g'(x)

A: Inverse of function problem....

Q: If f(x) 3 find f'(2). x²

A: Given that f(x)=3x2So, f(x)=3x-2

Q: Suppose that f(x) = f'(2) = -2 x6 Evaluate the following: ←

A: f(x)=-2x6d dx(xm)=mxm-1

Q: Differentiate. x2 -9 f(x) = In f'(x) = O

A: Explanation: Given that,  f(x)=lnx2-9x

Q: Find the function f(x) if f'(x) = ex+ 2 +(3/x) and f(1) = 6

A: We have to find the integral of f'(x) to obtain f(x) Steps: 1. Integrate with respect to x 2. Apply…

Q: Suppose g(x) = x²f(x) and it is known that f(2) = 5 and f'(2) = -2. Evaluate g'(2). g'(2) =

A:

Q: Let f(x) be a one-to-one function such that f(2)=5 and f'(2)=-4.  Find f(-1)'(5)

A:

Q: x-²²-3 ²-3, determine the x-value(s) where f(x) changes from concave up to concave down. f(x)= Ox=…

A:

Q: 3. Find f'(x) for f(x) = 3x-4 2x+3

A:

Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: Find f. f "(x) = x-2, x > 0, f(1) = 0, f(5) = 0 f(x) =

A:

Q: Given that h"(w) = -34. State the function that best describes h'(w). O a. h'(w) = -34w O b. h'(x) =…

A: Use the concept of power rule of derivative and select the option form given.

Q: Differentiate the function. f(x) = √√In x f'(x) =

A: Given

Q: Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values…

A:

Q: X=(1)+ wam (xf pulf Z-x7=(x)₂ + £I-E#

A: Topic = Integration

Q: x2 Find f'(x) if f(x) = 5x – 3

A: As we know that: The Quotient rule: fg'=f'·g-g'·fg2 The Power rule: ddx(xn)=nxn-1 Given: f(x)=x25x-3

Q: Let f(x) = -V5. Find f'(x).

A:

Q: If f is the function f (x) = + 4/x, then f' (4)

A: The function is  f(x)=4x+4x

Q: Find y' if x' = y*

A:

Q: Consider the function. Find f'(x). f'(x) = Find F"(x). f"(x) = f(x) = x³ - 3x² + 3 Find f"(-2) and…

A: We will use simple differentiation to solve it.

Q: The functions f and g are differentiable and h(x) = f(g(x)). Use the information below to find…

A: We know that If h(x)=f(g(x)) then h'(x)=f'(g(x))g'(x)

Q: 2. Find f'(x) for f(x) = x²e.

A:

Q: 7. Given the function 8(x)%3D4X' - 3x² +x-1, find g(0), g(-1), and g(x-x) |

A: Some important formulas (a - b)3 = a3 - 3a2b + 3ab2 - b3 (a - b)2 = a2 - 2ab + b2

Q: 2 7. Evaluate f' (-1) for f(x) =- x X3

A:

Q: Find f'(1) for the following function

A:

Q: Let y= f (x) be a function with f (4)=12 and f(4)= 0.5.

A: We have to find

Q: а. f(x) %3D х3 In x + cos x b. f(x) %3D logs(3х3 + 2х + 1) ((5х+1)6 Vx2+x с. f(x) %3D In

A:

Q: f(3.8) - If we knew that f"(x) < 0 on the interval (3.5, 4.5), would your estimate above be an…

A: We need to find f(3.8)

Q: Consider the following function: Step 1 of 4: Determine f'(x) and f"(x). Answer f'(x) = = || - 1x4 +…

A:

Q: Let f(x): f'(x) = and f"(x) = = 7x² 4 - 3x -. Then

A: Given query is to find indicated derivative.

Q: What is the f'(1) of the function f(x)%3D foralla #-1 x+1

A: We have to find