Calculate the derivative of the function. HINT [See Example 3.] h(x) = 3[(2x – 1)(x – 1)]¬1/3 h'(x)

Q: 1: Using the definition, calculate the derivative of the following function. S(x)=4-x²

A: Topic:- derivatives

Q: 1) Find the derivative of the given function with respects to e 3tan ở In 3 y

A: Given

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: Find the derivative of t(z)= (Z-2)5

A: fz=z-25z2+iz+12 Now find the derivative of fz f'z=ddzz-25z2+iz+12…

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

A:

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

A:

Q: 9. [Essay] Find the derivative of y = 3x + 1). За* (x? — Зх + 1). Зах

A:

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

A:

Q: 1. Determine the first derivative of the functions below with the rules for deriving the function:…

A: A Given function is y=4x3+32. Use formula ddxxn=nxn−1 Differentiate  y=4x3+32 by using the chain…

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: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 1. The derivative of b** is 2. The derivative of is Inx

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: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+ 1)

A:

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: 1. D, (x') 2. D, (5x) 3. D. (x-2x)

A:

Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: 4 Find the derivative of the function y= f(x)= Jx(x-8). %3D

A:

Q: Q2/ Find the derivative of the function f(x) = V3x +1 by definition %3D

A:

Q: 1. Find the derivative of the functions, do NOT simplify. a. y = In(8 – 3x) | b. y = ln /2.x + 1 3a2…

A: We have to pick the most challenging formula among differential formulas and solve it.

Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

A:

Q: Find the function with derivative f'(x) = e8 that passes through the point P= (0,7/8).

A: We are given a diierentrial equatrion[f'(x)=e8x ] and a pssing point (0, 7/8) of the same  we need…

Q: In (xv/x² + 7). n (xVx2 %3D · Find the derivative of the function y = In

A: To find the derivative of the Given function, we have to apply chain rule and product rule.

Q: Q. / Find the derivative of y = (In(x²))'n(x²).

A:

Q: 9. Find the derivative of y = xe3-x (A)e3-x? (B) 0 (C) e³-x*(1– 2x?) (D)–2xe³-x² (E) e3-x*(1+ 2x²)

A: Given : y = xe3-x2

Q: h(x) = (cos x)(4x²– 3)

A: Explanation of the answer is as follows

Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: Find the derivative of the function f (x) = /e* – In(x) 12 – 1/x) O (ex12 – 1) O (e2 – 1/x) e? -x)

A:

Q: Suppose h(x): . What is the correct result of the derivative of h with respect to x? 3x · In (5)…

A:

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

Q: 1. Using the definition of derivative, find the derivative of the following functions: (a) y = xvx²…

A:

Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

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: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

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

A: To determine the linearization for the function.

Q: Suppose the derivative of f exists, and assume that f(2) = 1, and f'(2) = 2. Let g(x) = x2f(x), and…

A: Apply the product rule to find the derivative of g(x) and then substitute the given values as…

Q: Find derivatives of the functions defined as follows: y = e-2x

A: The derivative of the function ex is ddxex=ex. Find the derivative of the function y=e-2x using…

Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

A: Since you have asked multiple questions in single request so we  will be answering only first…

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

A:

Q: Find the derivative of the function y = In(x /x² + 14 X Vx²+14 1 Vx²+14 1 x²+14 x2+14

A: Topic:- derivatives  Note:- as per our guideline if more than one question uploaded than only first…

Q: Monday, 1) Find the derivative of the given function with respects to e y = 3lan® In 3

A:

Q: Find the derivative of the function f(x) = 3x? – - 12x – 28 by definition of derivatives f(x + h) –…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: (n2 – 1)* 31. H (r) = (2г + 1)8

A: In the question it is asked to calculate the derivative of H(r)=(r2-1)3(2r+1)5 using chain rule.

Q: Find the derivative of the following functions by applying "Delta Metho Show your complete solution.…

A:

Q: 2. f(x) = 2x – 5x%

A:

Q: 7. Find the second derivative of the following function: y = e** +In(7e¯* + 5x³) – 5²× +-

A:

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

A: