8. The function f(x) = 4x + 3 is one-to-one. a. Find an equation for f, the inverse function. b. Verify that your equation is correct by showing that f (f(x)) : = x and f '(f(x)) = x.

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

A: Topic:- derivatives

Q: In the given question as follows/, find the second derivative of the function.   f (x) = (3 +…

A: f(x)=(3+2x)e-3x

Q: 4) f(x) e**+6x

A: If F(x) = f(g(x)) , then F'(x)= f'(g(x)).g'(x). dexdx=ex dxndx=n.xn-1. Quotient Rule of…

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: Find the derivative of the function. 3x 9(x) = e+5.

A:

Q: Consider the following function. Without finding teh inverse, evaluate the derivative of the inverse…

A: Given information:The given function is .

Q: 1. Find the function whose derivative is XV X xª – 1

A: We need to find a function whose derivative is 1xx4-1

Q: Consider y = f(x)=√1+2x, x 2-1/2. Without finding x = f(y) explicitly, find the derivative of the…

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Q: What is the first derivative of the following function: f(x) = (x³ + 2)4 O f'(x) = 12x²(x³ + 2)³ O…

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Q: Find the derivative of the inverse function s(x) if f(x) = -x+ 1 1 r + 1

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Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: Find the derivative of the function g(x)=(2x^2+2x+2)e^x g'(x)=

A:

Q: (14 Find the derivative of the function 7 (^ Y = x²+3 15 x²-3

A: Find the derivative of the function  y= [(x2+3)/(x2-3)]5

Q: Find the derivative of the function g(x)=(5x^2−3x+1)e^x g'(x)=___

A:

Q: Find the derivative of the given function from the first principle ax2+bx+c

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Q: Work out the derivative of each of the functions below> a. f(x) = 3 ( x - 5)4 + 121. %3D

A: Hi there, at a time we can answer only one question and the exact one was not specified. So, I have…

Q: Find the derivative of the function g(x) et 2 – 2x gʻ(x) =

A: We have to find derivative

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

A:

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

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Q: Find the derivative of the function g(x)=(3x^2−4x+3)e^x g'(x)=

A:

Q: 1) Find the hundredth derivative of p (x) = (x + x° + x')'º(1 + x²)'' (x³ + x° + x'). Justify your…

A: Here we have to find the hundredth derivative of p(x)=(x+x5+x7)10(1+x2)11(x3+x5+x7) .

Q: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

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

A:

Q: Find the indicated derivative for the function. h"(x) for h(x) = 2x "5 – 6x -8 h"(x) =

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

A:

Q: 6. Find the derivative for each function. b. f(x) In 5x3 2)3 f(x) (e*3 2) а.

A: Use exponent rule for exponent 3 and use chain rule for (e^x^3 +2)

Q: h(x) = (cos x)(4x²– 3)

A: Explanation of the answer is as follows

Q: Find the derivatives of the following function f(x) from the first principles  (i)x3

A:

Q: 1. Consider the function f ( x ) = 1 + 1/10 x3 + 1/25 x5 .  Select any point ( a , f -1 ( a ) ) on…

A: Given function : f(x)=1+110x3+125x5 To solve the given problem first we need to find the inverse of…

Q: Find the first derivative of the following functions and simplify your answer. 1.) y=( 5x-2' 2.)…

A: We will use the following formulas : (f(g(x))' = f'(g(x)) g'(x)  uv' = vu'-uv'v2 1.) y = x3+15x-24…

Q: 1. Find the first derivative of the following functions: y = f(x) = -(2x + x³)-2 + 4x (2x+4)² (a)…

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Q: f(x) = e*

A:

Q: 16. Find the derivative of the following function. 6x f(x) = 5e 7x f'(x) =

A:

Q: Find the derivative of the following function. f(x) = 4x -34x+ e 4 %3D

A: We will use some set of formulas of differentiation : ddxxn = n xn-1ddx constant = 0

Q: 11 8 Find the derivative of the function: y = 3(x – 4)' x-4

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Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

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Q: Which of the following is the derivative of the function f (x) = 5x · e*? Of (x) = 5e* Of'(x) = 5e*…

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Q: 1 If f(6) = 3, and f'(6) 2 Let f'(x) be the inverse function of f(x). (f ')'(3) = Write the equation…

A:

Q: Find the derivative of the function m: f(x)= e^x^3+4

A: Topic = Derivative

Q: Find the derivative of the function g(x)=(3x^2+2x+4)e^x

A: Given that: g(x)=(3x2+2x+4)ex

Q: 1 4. Use the definition of the derivative to compute f'(x) given f(x) = 2x 3

A: Given,          The function is fx=12x-3 .

Q: What is the first derivative with respect to x of the function g(x) = 3/9 9. O 1/2

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Q: Find the derivative of the following function f(x)=10x^4-32x+e^2

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Q: Find the derivative of the function g(x)=e^x/2−4x g'(x)=

A: Here we need to apply chain rule of differentiation. We have Derivative of e^x is e^x.

Q: 11.Find the derivative of the functions: a) f(x) = In(9x²2 – 3x) b) g(x) = In(ln x)

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Q: Find the derivative of the function g(x)=(5x^2+2x−1)e^x g'(x)=____

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Q: 22. Find the derivative of the following function. f(x) = 14x6 – 34x + e² f'(x) =

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

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

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Q: 2. f(x) = 2x – 5x%

A:

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

A: