Use the Chain rule to differentiate each function (a) f(x) = In(x +sin(x)) b) g(x) = (-2x² +3x + 1)3 c) h(x) = cos(3x² + 2x + 1)

Q: Solve for the derivative of the function using chain rule. 4. f(x)= (x3+4)5/ 3x4-2

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Q: Let y=sin2x. Differentiate this function without using the chain rule.

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Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

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Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: Differentiate: (etan(x)) /(1+x)  Show all working out.

A: Given  etanx1+x. We have to differentiate it. Used formula:- ddxfxgx=gx⋅ddxfx−fx⋅ddxgxgx2 Here,…

Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x²-6x+5.

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Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x³-8x+9.

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Q: f(x) = (6x² - 2x+1)^

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Q: In Exercises 20–21, find a formula for the derivative using the power rule. Confirm it using…

A: NOTE: Refresh your page if you can't see any equations. . take derivative (using power rule)

Q: Find the derivative using DELTA METHOD f(x)= 2x-x2

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Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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Q: of n'(x)= 2x-1/x2-x

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Q: Find the derivative. using chain rule 7 5. у %3 V1-14x2

A: The given function y=71-14x2

Q: x=1), 3. Y = In (x-1), (х-2)2

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Q: Find the derivative 2x %3D 1-x2 (1–x2)? 2 1-x2 (1-x2)? O None of these

A: We use Quotient rule to solve this derivative

Q: =) f(x) = x²e¬4x

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Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

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Q: Find the derivative using the limit process of f(x)=x² + 3x f(x)=x² +3x

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Q: fcac) fCre)ニ2x+5

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Q: Find first and 2nd derivative guncic 2 tan2x 3.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 1. f(x)=(2x-5) ¹ (4x+3)²

A: We need to find derivative.

Q: 2x-1 n' (x) = x2 –x

A: Given,          Anti-derivatives of n'x=2x-1x2-x

Q: Use the Chain Rule to express the second derivative of f ◦ g in terms of the first and second…

A: First, find the first derivative of the function, consider that the function f(x) and g(x) are…

Q: Find y" by implicit differentiation.   9x2 +y2 = 9

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Q: 1 3. f(x) = (-x4-3)2

A: Solve for the derivative

Q: Find the derivatives of the following functions using CHAIN RULE. f(x) = (4x2-5x)3

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

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Q: first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: Find the derivative of the function using Chain Rule. Given f(x)=(x²+x-3)√√x²+x-3

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) - 12x 1 1 In(arctan(x)) + In(6x² + 6x – 4)-…

A: The given function is fx=arctanxln6x2+6x-4

Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: Find the derivative. Using Chain Rule y = (2x2 – 1)3(3x² + 1)³ |

A: According to question,Given Function,y = 2x2-133x2 + 13

Q: f(x)=5e^−2x^3+8x^8 f'(x)=

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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 f(x) = (5x 2 + 3x + 1) × (3x 2 + 2x − 1) × (x 2 − 1). Show all steps.

A: Given:f(x)=5x2+3x+13x2+2x-1x2-1

Q: the Chain Rule.

A: Given: y=11-x46. Let, u=1-x4 By chain rule, the derivative of y with respect to x is given as,…

Q: f(x) = (x2 + x) (x* - 6x)3 %3D

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Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.) y=…

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Q: -f(x)=√√5x² +2

A: Please see the answer below.

Q: Find the derivative of the function.

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Q: Use the chain rule to find the derivative of f(x) = 4( – 5æ" + 3z")" %3D

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Q: 2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second…

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Q: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

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Q: Find the derivative of the given functions using chain rule. 1. f(x) = (2x + 1) 2. f(x) = (x² + 4x –…

A: To solve the following derivatives using chain rule and product as well as quotient rule.

Q: az and ax az Use implicit differentiation to find for x2 + 2y2 + 3z2: 1. ду

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Q: In x g(x) = 2

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Q: Find y' by direct differentiation (with respect to x). y=-x2+2x5-e-6x

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

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

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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.