Let f(x)= [(x+4)^5(4x-1)/(6x+3)^5]^1/6 Use logarithmic differentiation to find the derivative of f. f ' (x)= f (x) [A/(x+4)+B/(4x-1)+C/(6x+3)], where  A=______ B=______ C=______

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: 1) Using method of logarithmic differentiation, find the derivative of y = (2.x² + 1)(2=-3)

A: Given: Y = (2x2+1)(2x-3)

Q: x3491x-42 y%3D 26. Use logarithmic differentiation to find the derivative of (x- 1)64

A: The given equation is y=x3491x-42x-164. Take log on both sides and expand. lny=lnx3491x-42x-164…

Q: Use logarithmic differentiation to find the derivative of y. 7) y = 1 X - 7 1 (1 1 A) 2 x В) х- 7…

A: We use  Logarithmic properties

Q: (In z) dr and P -(a") = a* In a, dr Also, recall fundamental differentiation formulas or rules, such…

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Q: 1) Find the derivative of y =-+x-1 %3D

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Q: x³(1 – x²)² 2 4y = in (1+x²)²

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Q: 2. Find the derivative of (a) f(x) = x4 +2x-2 + 4ex

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Q: Find the first derivative of each function. a) f(x)=ln (e^x+e^-x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Use logarithmic differentiation to find the derivative of y. 2 3 (3x + 1)(x +2) y 3D (x4 + 5)(x+7)…

A: Given: y=3x+1x+22x4+5x+73 for finding derivative of given expression, first we take log both side…

Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: (A) Find an equation of the tangent line to the graph of f(x)=(4x+1)sin(πx) at the point whose…

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Q: 13. Find the derivative of y = in terms of f, g, h, f', g' and h', where f, g, and h are functions…

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Q: Use logarithmic differentiation to find the derivative of the following: 8. h(x) = 25x34x² ans.…

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Q: Use logarithmic differentiation to find the derivative of y = In(5x)'n(7x): y

A: Topic:- Derivative

Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

Q: Vsec- (z) In(z) Find using logarithmic differentiation for y

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Q: Use logarithmic differentiation to find the derivative of y. 3 (4x +1)(x+ y 3= + 3)2 3) V (xt+5)(x +…

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Q: Use logarithmic differentiation or an alternativemethod to find the derivative of the function  y =…

A: To find the derivative of the given function.

Q: Find the derivative of this complex equation using logarithmic differentiation?

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Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: (a) Use logarithmic differentiation to find the derivative of the function. y (In x)seca (b) Find an…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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

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Q: use logarithmic differentiation to find the derivative of y=(x^2+3)(x-1)^2(x-2)^1/3

A: Applying natural logarithm on both sides, we get

Q: 5. Use logarithmic differentiation to find the derivative of the function. (x²+1)6 tan² x y = X3

A: Explanation of the answer is as follows

Q: • Use logarithmic differentiation to find the derivative of y = f(x) = 1-x)²V4+x² (3x-5)* • Find the…

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

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Q: The graph below is of f "(x) for some function f(x) with domain (-∞, ∞) (i.e., the graph of of the…

A: Since you have asked a question with multiple question in a single request, we would be answering…

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: Using logarithmic differentiation, Show that y(x)=xa2xex2 has no stationary points other than x=0,…

A: Given function is yx=xa2xex2. We have to show that the given function yx has no stationary points…

Q: Find the derivative of f with respect to x of f(x)=ln x8.

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: if f(x) = x²√√In x² A. f'(x) = B. f'(x) = c. f'(x) = D. f'(x) = find the derivative of this function…

A: Given,            fx=x2lnx2xTo find : Find the derivative of the given function.

Q: Find the derivative of the function. h(x) = ln[(−6x + 3)(x + 3)]

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Q: Find the derivative using logarithmic.   sq root of ((x2-1)/(x2+1))          for x>1

A: Here given for x>1

Q: 1) Use the Product Rule or the Quotient Rule to find the derivative of the given function a – g(x) =…

A: The objective is to use the product rule or quotient rule to find the derivative of the given…

Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

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Q: Find the derivative of a function at a given point F(x)= 2e^x-x at x=1 F(x)= x^3-5x at x=2

A: We have to find derivatives of the function: Fx=2ex-x at x=1 and Fx=x3-5x at x=2. We know the…

Q: sin x.cos x- 8- Find y' for y = In x 9- Use the definition of differentiation to find the first…

A: Given  y=sin x cos x2ln x and f(x)=3x2 We need to differentiate these functions wrt x. This can be…

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: Use logarithmic differentiation to find the derivative of the function. y = (In x)cos 2x

A: To differentiate

Q: Use logarithmic differentiation to find the derivative of the function. y =  square root of…

A: Given: y=(x-5)x6+4y=(x-5)x6+412 While applying logarithmic differentiation , we take ln on both…

Q: Find derivative of: g(x) = sin(x-3x2)

A: Given query is to find the derivative of g(x).

Q: Find the derivative of the function h(x)= ln(5x+1/7x-2)

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Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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: Use logarithmic differentiation to find the derivative (3x + 1)*(x – 4) of f(x) = (x² + 1)° - sin(x)…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: