Compute the derivative of each of the following functions in the two ways given. F(x) = (1 + 2x)³ by a) expanding the binomial and taking the derivative of the polynomial and b) applying the chain rule.

Q: Find the first derivative: y = In V2x3-5 Oý = 203-5 O y = 4x2 203-5 3x2 O Ý = 23-5 O Ý = 6 52 y =…

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Q: 2x+1 S(x) = 3x+2,

A: Solution:Given     f(x)=2x+13x+23To find the derivativeFormula:ddx(xn)=nxn-1uv'=vu'-uv'v2

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

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Q: 6. Find the derivative for each function, and simplify (reasonably): a) j(x) = (3x² + 3x – 1)* b)…

A: According to the chain rule of differentiation:   According to the Product rule of differentiation:

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

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

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Q: . Get the derivative of the given function. 2. y - In 7x

A: Solving the problem by finding the derivative of the function.

Q: Find the derivative of the following using First Principle. 4) y = -2x2 + 3x – 12 5) f(x) = x2 + 15x…

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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 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: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Compute the derivative of the following function. 1(x) = 3e 3x f'X)%3D

A: Topic - differentiation

Q: c) h(x) =(5x-1) 12x² – 6 d) m(x) = (4x² – 9x} %3D

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Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (2) — 5а — 4 %3D | 2. f…

A: Recall: Derivative using Four step Rule:step 1 : Write f(x+h) and f(x).step 2 : Compute f(x+h)-f(x)…

Q: 2. g'(x) where g(x)= x² +7x-5 %3D

A: ddxxn = n·xn - 1, and ddxC =0

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

A: Given that: The function f(x) and its first derivative have the following values at x = 0 and x = 1.…

Q: Compute the derivative of the given function. f(x)=−4x^π+4.1x^1.3+π^1.3

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Q: Find the derivative of the function. (3x +5) f(x) = In (7x + 5)*(2x+ 8) 14 2 O a. 3x +5 + 7x +5 2x…

A: We have to check

Q: 4. Find the second derivative for the following functions: a) (ans.:6x +

A: Derivatives

Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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: Find the derivative of the following with respect to the given variable 3. 6x (2x-5) 4. (3x - 4x)…

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Q: Find the first derivative with respect to the domain variable for the following functions. 4. f(x) =…

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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 the derivative of the function. y= log , (3x2 - 2x) 5/2 O A. In 9(3x- 1) (3x2 - 2х) OB. 10(3x –…

A: We need to apply 1.chain rule 2.differentiation of logarithmic   we get option c as correct answer

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: 1. Find the derivative of the following. f(x)=13x* –7x³+5x²+11x+75 b. S(x)-(x*+2x*+4)(x"-3) 3x -6x+7…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 7. Find the derivative of each funcrion. a. y = 5-4* b. fCx) = xqx d. FCx) = Togax-1 C. Y =…

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Q: find the derivative of each of the following:  f(x) = x^2 + 2x - 3 / x^4

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

Q: Find the derivative of the following function x4 F(x) = (2t – 1)3 dt using the Fundamental Theorem…

A: Consider the given function in the form of the definite integral for f(t).

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: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: Solution :1.fx=23x3-2xfirst derivative ,f'xf'x=29x2-2Second derivative…

Q: Find the derivative of the following: 1. D, (x³) 2. D, (5x2) 3. D, (x – 2x*) 4. D, (x-2)(2x +3) 5.…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: Find the derivative of the following function by first simplifying the exp x2 - 64 g(x) = x-8 ....…

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Q: y = log4 x %3D .y = In(5x2 -4x + 8) %3D

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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: Find the derivative of the given function 4. g(x) = (4 – 9x²)³ 3 5. h(x) x+5 = x2-9, 6. A(x) = v3x³…

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Q: Compute the derivative of the following: 3 g(x) = 5 2x'x 4.

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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 the derivative of the following with respect to the given variable 5. x+6 5x+4 6. 4x2- 9

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Q: Find the derivative of ?, implicitly of  BY SHOWING ALL STEPS When N=11 and M=3

A: Given that lnMxy-tanNx+My=e-M-MyN And N=11 and M=3

Q: Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h)…

A: Given: The formula is f'(x)≈112h -f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h). To prove: The given formula. To…

Q: Determine the anti-derivative of the following functions: a) S(x)=(3x+2)(2x* - 3x +4)

A: Given, f(x) = (3x +2)(2x2 -3x +4) So  f(x) =  6x3 -9x2 + 12x + 4x2 -6x +8     f(x) =  6x3 -5x2 + 6x…

Q: a derivative computation using the FTC and the chain rule t): df 13

A: Given : ddxFx3 =ddx∫13x3e-t2dt

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: 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: Зх +1 a) y =- 1 b) g(x)= Jx -

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

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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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