we define the first difference δf of a function f by δf (x) = f (x + 1) − f (x). Show that if f (x) = x2, then δf (x) = 2x + 1. Calculate δf for f (x) = x and f (x) = x3.

Q: Moreover, suppose F(x) = f(g(x)) and G(x) = g(f(x)). Use the chain rule to calculate the following…

A: f(x)=cot x  and  g(x)=5x-2

Q: find all possible functions with the givenderivative. y' = √θ

A: We first separate the variables

Q: Find the derivative of the composite natural exponential functions 1. f(x) = In( 2. g(x) = In(v³ +1)…

A:

Q: Find f"(x) for a) f(x)= lnx - ln(1/x)

A:

Q: .) What is the inner and the outer functions? b.) What is the derivative o

A: Given : The function is f(x) = x2+ 3x +1 .

Q: When we introduced the quotient rule, we didn't actually prove it. Let's do that using only the…

A: Given Data: Function: fxgx=fx·gx-1   The chain rule for derivative is, ddtfgt=f'gtg't ......1   The…

Q: Find the average rate of change of f(x) = x2 from x1 = 1 to x2 = 2

A: The average rate of change formula is:

Q: If f(x) = and g(x) = Vx, then the derivative of f(g(x)) is -VE (A) ( + 1) (B) -(x + 1)- -2x (C) ( +…

A:

Q: find the net change in g between x=0 and x=7

A: Here we have to find the net change.

Q: Find the average rate of change of g(x) = – 3x² +1 on the interval [– 1, 4]

A:

Q: Use the graph of the first derivative function f'(x) to find x values at which function has relative…

A: First of all, consider the graph of f '(x).

Q: Find the average rate of change of the function f(x) = x^2 + 3x from x1=5 to x2=6

A:

Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

Q: Given F(x)=1/X+2,  find the average rate of change of  f(x) on the interval [2,2+h

A:

Q: Find the average rate of change of the function f(x) = x² -3x + 5 between x = 0 and x = 2.

A:

Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = 2x² ,…

A:

Q: Find the average rate of change of the given function on the interval [0,3]. F(x)=-x^2+2x+2

A: Topic = Functions

Q: If (x1, f(x1)) and (x2, f(x2)) are distinct points on the graph of a function f, the average rate of…

A: If (x1, f(x1)) and (x2, f(x2)) are distinct points on the graph of a function f, the average rate of…

Q: Suppose / (x) = /e*, Evaluate: /f(x) dx

A: Givenf(x)=ex

Q: Find the average rate of change of the function from x=1 to x=2.   f(x)= -6/x^2

A: As we know that the expression for the average rate of change of the function: Average rate of…

Q: Find the SECOND derivative of the given function. (b) g(x) = x+2

A:

Q: Find the average rate of change of the function from x = 1 to x = 2. f (x) = - 14

A: Using function notation , we can define the average rate of change of a function f(x) from  x = a to…

Q: Which function has the same derivative function f(x) as g(x) = lnx + x² – x? Select one: O a. f(x) =…

A: Given: g(x)=ln x+x2-x The derivative of ln x is 1x. The rule for differentiation is ddxxn=nxn-1…

Q: Find the average rates of change of f(x) = x2 + 2x (a) from x1 = −3 to x2 = −2 and (b) from x1 = −2…

A: (a) Average rate of change of f(x) from x1=a to x2=b is given by f(b)-f(a)b-a f(x)=x2+2x Find f(-3)…

Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…

A: Given function: gx=4e3x5+2x Differentiate the above function w.r.t 'x' g'x=ddx4e3x5+2x

Q: Find the average rate of change of the function f(x)=−2x^2+5 between x=−1 and x=3

A: given function :

Q: find all possible functions with the givenderivative. y' = x

A:

Q: 3. Find the derivative of the following function using the formula. S(x + h) – f(x) lim a. f(x) =…

A:

Q: Find the average rate of change of the function:  f(x) = 6x from x1 = 0 to x2 = 4

A: fx=6x Now, f0=60=0 & f4=64=24

Q: 2. Find the derivatives: (a) f(x)=(x² - 2x+1) (x² -1) x+2x+5 (b) f(x): %3D x² +1

A: Part (a) Given a function Using product rule of the derivative

Q: Given the function g(x) = x² - 4x + 0, determine the average rate of change of the function over the…

A: GIVEN DATA : Function gx=x2-4x+0  TO FIND : Average value of gx on the interval 1≤x≤7 In order to…

Q: Find the average rate of change of f(x)= x2 +3 on the interval (0,2).

A: Given:

Q: Find the average rate of change of the function f(x)=6x from x1=0 to x2=2.

A: Given, x1= 0 X2= 2 f(x)= 6x

Q: Find the derivative of the function f(x) = Jet – In(/x) (e+12 – 1) O (e:/2 – 1/x)

A:

Q: Find the average rate of change of the function over the given interval  f(x)= 3/x-2 ; (4,7)

A:

Q: 9x Find the derivative of the function f(x)=In x2+15 2x O f'(x)= x²+15 15-x2 f"(x)= x2+15 2x O…

A:

Q: The derivative of the function f(x) = 5+ ln r is: 1 a. f'(x) = 2.x/5+ In x b. f'(x) = 2/5+ In x In x…

A:

Q: find the average rate of change of g(x)=x3-2x+1 from 1 to 3.  average rate of change for function…

A: Given: g(x)=x3-2x+1 over the interval [1,3]

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To find a linearization at a suitable chosen integral near a= 0.11 at which the below function and…

Q: The derivative of the function y = (x² – 1)2 (x² + 2)³ is LA. 2x (x² +2)°(x² – 7) 2x (x² + 2) (x² +…

A: As we know that; The Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The chain rule:…

Q: Find the average rate of change of the function from x1 to x2. Function x-Values f(x) = -3x3 + 3x? +…

A: Recall: Average Rate of Change of a Function :        Ax=f(b)-f(a)b-a; where , f(a) and f(b) are the…

Q: Find the average rate of change of the function:f(x) = x2 + 2x from x1 = 3 to x2 = 5

A: Given function is fx=x2+2x. To find: The average rate of change of the given function from x1=3 to…

Q: Find the derivative of the given function e5x (2x+1)5 b. f(x) = In Vx²+1 f(x) = (x In x – x)

A: Given that: b. f(x)=lne5x(2x+1)5x2+1c. f(x)=(xlnx-x)

Q: Find the average rate of change of f(x) = x2 from x1 = -2 to x2 = 0.

A:

Q: Find the average rate of change of the function g(x) = x³ – 7x + 9 from x = 0 to x = 3.

A:

Q: Compute the derivative function f'(x) algebraically. f(x) =x²-9 O a. f'(x)= 2x O b. f'(x)=2 O c.…

A:

Q: Find the average rate of change of the function from x1 to x2 f(x)= 5x+7  from x1=-1 to x2=0

A:

Q: Find the average rate Of change of.. f(x)= x²-1xI [3,2] on

A: Given: fx=x2-x, x∈2,3 we know that average rater of change of a functionfx on interval a,b is given…

Q: 2. Consider the function f(x) = e¯*. -2x (a) Show that the derivative is f'(x) = %3D

A: