Find the inverse of ƒ (x) = –7x – 4. f '(x) =| O

Q: Find the derivative of each function e 2x a. f(x) = 2x+1 b. f(x) = In Vx + 2x c. f(x)= x²e* – 6x

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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: Find the derivative of F(x) = f (t³ - t) ³ dt. O 5 (t³-t) (3t²-1) ○ (x³ - x) 5 ○ 5 (2³-x) 4 O 3t² -…

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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: Find the derivative of y with respect to x, t, or 0, as appropriate. y=x" In x - O A. 4x-x O B. x*…

A: The function is given as y=x4 ln(x)-13x3 Differentiate the above function w.r.t 'x' y'x=ddxx4…

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: Find the second derivative of the function y=x(x² – 1) (А) 4x(5х2 - 3) в) 2x(5x2 - 6) (с) (2х -…

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Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

Q: 2. √√√x + y + xy = 21

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

A: Topic - differentiation

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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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: Let y = f(x), where f(x) = (x-4)/(x^2+4).   Find the differential of the function.

A: Calculation: The first derivative of f(x) is given by

Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: Find the derivative of the function.s(x) = e3x − 1/x3 − 1

A: The given function is

Q: Find the derivative of the inverse of f(x)= x° +1 using the formula dy 1 off "(x)= g'(x) =- f'(g(x))…

A: Topic:- application of derivatives

Q: Compute the derivative of the following function. f(x) = 3x e 3x f'(x) = O

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Q: A. Compute the derivatives of the following functions 1. f(x) = xe3x-sinx %3D

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: f. y=In(x8+1)

A: We will solve the problem

Q: Find the derivative of the function. F(x) = In(4 – x®) %3D f'(x) %D

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Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

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: Q4: Find the second derivative of f(x) = %3D (cos^2) 7x: *

A: The given function is;  f(x)=cos2(7x) We have to find: f''(x)

Q: 3 Find the derivative of the inverse of f(x) = x +1 using the formula dy %3D 1 off "(x)= g'(x)= dx…

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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 the function f (x) = /e* – In(x) 12 – 1/x) O (ex12 – 1) O (e2 – 1/x) e? -x)

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Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

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Q: Find the second derivative of f (x) if ƒ (x) = (2x + 3)* %3D A) 4(2x + 3)³ (B) 8(2x + 3)3 (C) 12(2x…

A: Proceed as shown...

Q: Find the derivative of the inverse of f(x) = x' +1 using the formula dy 1 * of f"(x) = g'(x) = dx…

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Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

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: dx = +C (x+1)² X+1

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Q: (x3-x)² .3. 2 5. у 3 х+1

A: We’ll answer the 5th question since we answer only one question at a time. Please submit a new…

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: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: Find the derivative of the following function with respect to x. V5x + 8 V1– 9 cos (4x) - h (x) =…

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: Find the derivative of each function e 2x a. f(x) = 2x+1 b. f(x) = In Vx + 2x %3D c. f(x)= x?e* – 6x…

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Q: Find the second derivative of vx - Jy= 4 when x = 1. 2 1 -1 -2

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Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

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

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Q: Given f(x) In(5x) the derivative 5 f'(x) is 1 5x 1 5x O 5 O x5x 1

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Q: Use the u-substitution to find the anti-derivative of h'(x)= xcos(2-3x2)

A: h'(x)=xcos(2-3x2) Formula ∫cos (x) dx= sin (x)+C

Q: Find the derivative of the function. y = In) x +6. (a)"* g(x) = log,(x) 9'(x) = (b) y = x5x + 2 (c)

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Q: Find the second derivative of y with respect to x if y = x In(x) - X. А.X In(x) B. In(x) C. In(x)/x…

A: The given function is y=x ln(x)-x

Q: Find the first and second derivatives of the function. 14. f(x)= x to the 7/2+x to the 5/3-x to the…

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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: Find the derivative of the given function. 5x y= In 6+x dy xp %3D

A: SOLUTION-

Q: Use implicit differentiation to prove that d/dx [ xn ] = nxn − 1

A: Here we use implict differentiating to prove thatddxxn = nxn-1

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.