Let k be a fixed positive integer. The nth derivative of 1/(xk − 1) has the form Pn(x)/(xk − 1)n+1 where Pn(x) is a polynomial. Find Pn(1)

Q: Find the differential of the function y=(3-x8)1/2

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Q: • Find f (x) of f(x)=by using the definition of the х-1 derivative. • 1- Find if y=3t-4 and t = Vx +…

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Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

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Q: Use the u-substitution to find the anti-derivative of m'(x)= 1/xln(x)

A: solution :- antiderivative is the integration  So put ln(x)  = u Then (1/x )dx  = du And then…

Q: Compute the derivative of the given function. g(t) = 2t - In(2 – 5t) %3D

A: Given that: g(t)=23t.ln(2-5t)

Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-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: Find the derivative of the following: 1. y=x(V1- x³ ) 1+x 2. у-. 1-x (x³+5) V4-x² 3. у — x*-x2+6 sin…

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Q: Find the third Taylor's polynomial f(x) = x3 – x² + 3x + 1 which can easily find the derivative at…

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Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

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Q: Find the derivative of:  a. 1/x^3 + 3 1/ square root of x b. x^3+2x over x^2+3x+ pi^2 c.…

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

Q: S-2(x-1 - x²) dx 5.

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Q: 2) Find the derivative of the following: c) cos 2x - 3) In(8x - 5x +2)

A: Given:         cos(2x−3)ln(8x2−5x+2)

Q: 2. g'(x) where g(x)=x² +7x-5 %3D

A: In this question we need to find a derivative of the given function.

Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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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: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: 55. By normalizing the function f(x)==-defined in the domain [0, 2], we will get as a result the…

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Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

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Q: • Find f (x) of f(x)= by using the definition of the x-1 derivative. • 1- Find if y=3t-4 and t Vx+…

A: we have to find the derivative using definition. as per definition  f'(x)=limh→0f(x+h)-f(x)h

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

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Q: Find the derivative of the function. g(x) = In| 8x – 9 | a. 8x -9 Ob. Sx -9 O. none of these 1 Od. -…

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Q: Find the derivative of y with respect to x. y=x* In (x) - O A. x* In (x) - x² + 5x* O B. 6x -x OC.…

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Q: (1) For every natural number n, x" = nx"-1 (you may use the product rule for derivatives and that x…

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

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Q: 4) Find the derivative of each function. a. f (x) = In(x² – 4) In e c. f (x) = b. f (x) = x² ln x

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Q: In (4x+7) 1. Find the derivative of f(x) 5x e 10-18 x? Evaluate the integral: 5x-3x 5 6x*-3x?…

A: Please see the explanation below

Q: Find the derivative of the function ffor n = 1, 2, 3, and 4. sin x fx) = - (X), I n =4 Use the…

A: Solve for the derivative

Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

A: f(x) = xk and we need to find all the derivatives of f(x)

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: 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…

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Q: Find the derivative of the function. 92-4x + h(x)= e 18x – 4x2 –1 92-4z++ x2 O b. 9x - 8x² – 1…

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Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given, f(x)=sin(2x)+17

Q: Suppose h(x) =23r +1 What is the correct result of the derivative of h with respect A h'(x) =3-23x +…

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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: Find the derivative of g(x) = J2x u²+1

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Q: Find the natural domain and the derivative of the given function. (a) ln(4x + 2) (b) x · cos x (c)…

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

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Q: 1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x –…

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Q: What is the first derivative of p(x)=6e^−8x

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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: 2 Find the derivative of the following function f(x)=2x-10x -8 using the limiting process a.…

A: The function is given by f(x) = 2x2-10x - 8 To evaluate : The derivative of the function using…

Q: Find the derivative of the function x³(2x + 1) f(x) = In x2 – 3 Select the correct answer below: O…

A: We can make it easier for you.

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

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Q: Consider the function f(x)=ln (1+x2). a. Find all the critical values of f(x)=ln (1+x2). Using the…

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Q: Find an expression for the nth derivative of f(x) = xe² by computing the first few derivatives,…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: