Using the fact that In[u(x)v(x)] = In u(x) + In v(x), use the chain rule and the formula for the derivative of In x to derive the product rule. In other words, find [u(x)v(x)]' with- out assuming the product rule.

Q: Differential function of x2 + 2x + 3tanx

A: The given function is: x2+2x+3 tan x

Q: Using the fact that Inſu(x)v(x)] = In u(x) + In v(x), use the chain rule and the formula for the…

A: Given: lnuxvx=ln ux+ln vx

Q: Using the Chain Rule, compute the first derivative of sin T-x.

A: We have given a composite function and we have to find derivative of function by using chain rule of…

Q: Find the derivative of y with respect to x. (Hint: chain rule) y = -csc-1 24 V(8x + 92 - 9 24 (8x +…

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Q: 11) Find the derivative of y = 3x (2æ² + 5x) Use two methods: Product Rule and Foil First method

A: Find the derivative of y

Q: Use the Chain Rule to express the second derivative off o gin terms of the first and second…

A: Let y=f o g then we have to find the second derivative of y.

Q: 2x+1 Ise Derivative Rules to find the derivative of g(x) x2-1

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Q: Find the local maximum, minimum and saddle points of the function using the second derivative test:…

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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: How do you find the derivative using the chain rule?

A: The given equation is hz=ba+z29.

Q: Using the limit definitoin of the derivative, comput the derivative of the function. x^3+3x^2+x+3…

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Q: Can you help me with this problem step by step?

A: The equation is given by

Q: 8. Find the derivative of f(x) = (1+x³)' ( 14x + - ) using differentiation rules.

A: topic - derivative of a function

Q: 75. F(x) has a negative derivative over (-, 2) and (5,9) and a positive derivative over (2, 5) and…

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

Q: I need help with e. and f.      JUST THESE TWO PARTS

A: First of all, we define F(x) as a composite function by identifying the inside function h(x) and…

Q: 6. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: By using differentiation. and definition of tangent at point.

Q: Find the derivative of the function by the limit process. f(x) = 6/x^2

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Q: Using limit definition of derivative, prove d/dx e^x=e^x

A: We using limit definition

Q: 28. Using the method of "First Principles" and showing all steps, determine the -3 2x-1 properly…

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Q: 9) Find the derivative of y = (4x + 3æ²) (6 – 3æ) Use two methods: Product Rule and Foil First…

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Q: Using the fact that u(x) = In u(x) – In v(x), In v(x) use the chain rule and the formula for the…

A: lnu(x)v(x)=ln u(x)-ln v(x)Formula:ddxln f(x)=1f(x)f'(x)

Q: firm produces a monthly quantity of a product given by the production function P(x) = 2000√x, where…

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Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: Determine whether the following statement is true or false, and explain why. The chain rule is used…

A: Given: The chain rule is used to take the derivative of a product of functions.

Q: fcac) fCre)ニ2x+5

A:

Q: Find the derivative of y with respect to x. y = csc-1(x5 + 1) ; x > 0

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Q: 4) Use the Chain Rule instead of the Quotient Rule. 4 Find the derivative y= 2x +1

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Q: 17. f(x) = x2 + x – 3

A: Answer is f'(x)= 2x+1. Explanation is given below using the limit process....

Q: f f(x) = x²√Inx² x . find the derivative of this function f'(x) 1-In x² x²√√In x² A. f'(x) = B.…

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Q: Find the derivative of ?(?) =5/13sin2(5?). using the chain rule

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

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

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Q: Find an anti-derivative for each function in C equals zero

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Q: 04:- Use the Chain rule to find the derivative ) of z = 3x2 - 2 xy y and If x=x (u, v) = 3u + 2v and…

A: Please refer to the image below.

Q: How do you prove the general power rule of derivatives using the inverse property (x^n=e^(nlnx))?

A: The general power rule:

Q: Using method of sub., find the Anti-derivative 1 x In x

A: detailed solution is given below

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

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Q: Find the derivative of f (x) = coth³(1In(x³)). %3D A 9x²coth?( In(x³)) csch2(In(x³)) - 9coth (…

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Q: Find the first derivative of y=3x^2-2√x

A: We have to find the derivative from the given function

Q: 2) Use the chain rule. (Chapter 2.5) Find the derivative y= (x² +3x)*

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Q: 31. Using one-sided derivatives, show that the function f(x) = {2. [x² +x, | 3х — 2, х> 1 does not…

A: Given: fx=x2+x     , x≤13x-2   ,  x>1

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: the function f(x) = In 5x +3x + 13). 6. Differentiate ° 7. Find the derivative of the function .2 y…

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Q: compute the derivative. 19. y=(2cosθ+5sinθ)9

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

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Given f(x)=x(x-1). a) Find first derivatives of function f(x) using product rule and chain rule.

A: Our objective is to find the derivative and critical points.