If f(x) = 12x2 - x3, what is the rate of change of f'(x) at (-1, 13)?

Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

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Q: 14. If x2 + y2 13, find at (2, 3). dx2 %3D

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Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: Find the derivative of x/ex^2.

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Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

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Q: Find the derivative. 2 - - dy dx - if y(x) = 1 x + 3 dy dx ||

A: This question is based on Chain rule diffrentiation. d/dx{f(x).g(x)} = g(x)d/dx{f(x)} +…

Q: ) y = In³ )) (tanh²(scc '(x²)

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Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

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Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

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Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: If the sign of the first derivative function is positive, the main function f(x) is decreasing.

A: We have to tell If the sign of the first derivative function is positive , the main function f(x) is…

Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

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Q: Determine the first derivative of the ff. function 1 + In(3x?) y : 1+ In(4x)

A: the given function is: y=1+ln3x21+ln4x we have to determine the first derivative of the given…

Q: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: 8. Find the derivative of y = x arctan 2.x --In(1+4x). -- - 4.

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Q: 3. Find the second derivative of y= xlnx

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Q: Find the derivative of z=(ln5)e^x dz/dx=

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Q: Find the derivative Of U-5

A: Derivative of integration

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

Q: What is the derivative of: y ln x − x ln y = 1

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

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

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Q: 5. y=x3 Find derivative ldv 4.

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: Find the second derivative if y = sinh- (n + x') at x = 0

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Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

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

Q: What is the difference of antidifferentiation and anti-derivative?

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Q: The derivative of y = -ln(cos(ex + 1)) is

A: Our Aim is to find the derivative of y=- ln cos ex+1 -(i)

Q: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: Find the derivative of the function y = x tanh−1 x + ln√(1 − x2)

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Q: Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on  [−2,…

A: To Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on…

Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: What is the first derivative of f(æ)= ln(3z²+7z )? 5z

A: Given  f(x)=ln3x2+7x5x We know that derivative of ln(x)=1/x…

Q: 4. y=ln(4x' +5)

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Q: Shows the derivative function of: x³  + ln x(3x² + 5)

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Q: what is the second derivative of -y/x

A: Apply the quotient rule, If f=uv,thenddxf=vdudx-udvdxv2 If f=-yx, where y is the dependent variable,…

Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: 9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7

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Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

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Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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