Example C.W: by using the definition of the derivative, find dy/dx of the function 1- f(2) f(x) = x²+ x + 1 3 2- f(x) = x - 1 3- f(x) - /x +1

Q: h(x)=In( x² ) +(x³-1 ) es*-10 Calculate the derivative at x=2, that is h'(2)=

A: Use chain rule of differentiation First differentiate with respect to x and then put x =2

Q: 1. If y = x³ + x - 5 then what is the derivative of y with respect to x?

A: Derivative of a function

Q: Find the derivative of the function.

A:

Q: 1. Find the derivative of each of the following functions using chain rule: y=3x* (x* -2) a)

A:

Q: 1. Find the second derivative of the function. 8(x) = 3\/x + e7*In(x)

A:

Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

A:

Q: A graph of y = f(r) is shown. In the same coordinate system, sketch a graph of the derivative…

A: To draw the graph of the derivative of the function

Q: Determine the derivative of y (x) = ( 3 x² + 11 x + 4 )³ e-6 x with respect to x. y '(x) =

A: topic - derivative of a function

Q: Find the derivative of the function. g(x) = e-X + 3e2x - 2e-x + 11 g'(x) =

A:

Q: Find the first derivative of each function. a) f(x)=ln (e^x+e^-x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: if f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1, then the derivative of f(x).g(x) evaluated at x =…

A: Given: f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1

Q: Compute the derivatives at the given value of a g(x)=(3x-5)/(x-2)     a=1

A:

Q: Given y = (ax? + bx )e -bx where a and b are constants. Find derivative of y with respect to x. e-bx…

A:

Q: Calculate the implicit second derivative of b(z)=(x-5)^2 find the value of b''(-1

A: find the second derivative of the given function

Q: Question 9 Suppose 8 (x) = sec-(x²), what is the derivative of g with respect to x? 2x A 8 (x) =…

A: We need to find derivative.

Q: Find derivatives of the functions defined as follows: y =(3x3 - 4x)e-5x

A: Given:          y=3x3-4xe-5x Let:  y=f(x)=3x3-4xe-5x Product rule of differentiation is given by…

Q: EXAMPLE 2 Find the derivative of the function below. g(x) = 3 + t2 dt SOLUTION Since f(t) 3 + t2 is…

A: To find the derivative of the function

Q: Question 31 Compute the derivative function f' (x) algebraically. f (x) = -5x³ + 7 O f' (x) = –15x²…

A:

Q: if f(x) = x²√In x² x . find the derivative of this function f'(x) A. f'(x) = B. f'(x) = c. f'(x) =…

A:

Q: Find the derivative of the function y = In(5e – 9xe "). y = ||

A:

Q: Example 7: Find all of the second derivatives for f (x, y) = 3xy2 + 2xy + x2. %3D

A:

Q: |(x+ 1) |(x – 1) Find the derivative of k(x) = ln A. k'(x) = x2-1 -1 В. К(х) — (x²+1)

A:

Q: Find the derivative of the function. y = (x + 1)²(x² + 1) ~ 3 ...... - 2(x + 1)(2x² – 3x – 1) OA.…

A: Given:- y = (x+1)2(x2+1)-3 To find :- Derivative ol y

Q: Suppose f(-3) = 3, f'(-3) = 5, = -8, and %3D g(-3) = 1, gʻ (-3) = H(x) = f(x)e®(x). Find the…

A:

Q: -3- 6. USE THE ALTERNATIVE FORM OF THE DERIVATIVE TO FIND THE DERIVATIVE (IF IT EXISTS) OF f(x) = x²…

A:

Q: What is the derivative of y = (x2 + 1) e-3 ? O y = (x² +1) (e-3) + xe² - 3 O y = (x² +1) (e*-3) +…

A: It is required to find the derivative of the given function.

Q: Find the derivative of the composite natural exponential functions 1. f(x) = In x² x-2 2. g(x) =…

A:

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: here x-intercepts are x=-3 and x=1 so the factored form of the parabola is…

Q: A. Find the derivative of the given function at a given number 1. y =3x -2 at f(1)

A:

Q: 4 a. Use implicit differentiation to find the derivative dy/dx of the given function. b. Find the…

A: The objective is to find the derivative and slope at the point .

Q: What is the value of y' at x=-4 is ______? Evaluate the derivatives of the given function for the…

A: The function is given by y = 5x2-x+53-3x-x2 To evaluate : The value of y' at x =-4

Q: 3. Find all possible functions with the given derivative y' =- 2

A:

Q: Example3: a) Find the derivative of f(x.r.:)= r - -: : at P(1.1.0) in the direction of 1= 2i-3j-6k.

A:

Q: Find the derivative of the function g(æ) = (5æ² – 4x)e" - g'(x) =

A: →duvdx = udvdx + vdudx→dexdx = ex

Q: Find the derivative of: y = 4x^2 – 1/x   y’ = 2x – x^(-2) y’ = x^(-1) + 8x y’ = 8x - x^(-2) y’ =…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The derivative of the function y = In (* + 1) (* - 1) is O y = O y = :- - 1 e+1 + -2 +1 ||

A: Question is solved.

Q: 5. a) Find the first order derivative of the following function. y x° In x

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: A graph of y= f(1) is shown. In the same coordinate system, sketch a graph of the derivative…

A: The given graph is of a parabola with the vertex (0,-1). So, its equation is:…

Q: Compute the derivative function f' (x) algebraically. f (x) = -5x3 +7 O f' (x) = -15x O f' (x) =…

A:

Q: 25. Find the derivative of the function. y = (1+ 3x)e - 3x O A. - 9e - 3x 3x В. - 3(1 + 3х)е - 3x -…

A:

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

A:

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: NOTE: Refresh your page if you can't see any equations. . the given graph is a parabolic graph and…

Q: 1 Find the derivative of each function: b) f(x)=(x'+3x² +7)° 2x+1 b) f(x)=- (x+2x)°

A:

Q: Find the derivative of the function g(x) et 2 + 3x g'(x) =

A: Given: gx=ex2+3x

Q: y = (4x + 3)/ln[2x2 + 3x - 5] y = 3( e2x + e-2x )(x2 - 4

A:

Q: Example: 1. Find the derivative with respect to x for the following. a. y= e3x2-1 b. f(x) = ee c. y…

A:

Q: Example 2. Find the derivative of the following with respect to x. x" +1. (iv) x-5 (i) x12 + 7, (ii)…

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: g(e) = . Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.…

A: