Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

Q: Estimate the instantaneous rate of change of the function f(x)=−x2+4x−4 at x=1 using the average…

A: Consider the given function f(x)=−x2+4x−4

Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: Find the maximum rate of change of f at the point (, 1).

A:

Q: Find the first derivative of the function y = 2ArcsinV(x/2) %3D

A: Consider the given function, y=2Arcsinx2 It also can be written as, y=2Arcsinx2=2sin-1x2

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

A: Please refer to the image below

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

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Q: Find the derivative of function. y = log(2x)

A: A composite function is differentiated as follows: ddxfgx=f'gx·g'x

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

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Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

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: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

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

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Q: What is the instantaneous rate of change of the graph of y = = cos x when x= 2n?

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Q: x + x dx x2

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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: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Find the second derivative of the function.

A: Given: fx=sec x To Find: The second derivative of the given function

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

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Q: Find the derivative of the function g(x) = log3 √(1 − x)

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Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

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: What is the instantaneous rate of change of f(x) = V +2-3 at %3D x = -2?

A:

Q: Solve for the derivative of y = x(e*) %3D

A: Find your answer below

Q: What is the derivative of a constant function?

A: The derivative of constant function is always zero.

Q: Find the derivative of the function. 2 x* + 2 .2 y 2 y' =

A: y = x2+2x2-25we know:ddx xn = nx(n-1)ddx f(g(x)) = f'(g(x)) . g'(x)

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

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Q: (d) y = xnz²

A:

Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: The size of a population of butterflies is given by the function. p(t)= 6000/(1+49(0.6)t) where t…

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Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

A:

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

A: Rate of change.

Q: The derivative f'(a) represents the instantaneous rate of change of y = f (x) with respect to x when…

A: Given that we need to check  behaviour of  the statement " The derivative f'(a) represents the…

Q: Find the second derivative of the function. f(x) = sec x * "(x) = Noc

A: Please see the explanation below

Q: Find the instantaneous rate of change of y =- at x = a

A:

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

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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 thousandth derivative of f(x) = xe -x

A: Given function,  f(x) = xe-x  To find the thousandth derivative of f(x)

Q: Calculate the derivative of f1 (x) = √1−2x by using the definition of the derivative as the limit of…

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Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

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: . Use a similar procedure to estimate the instantaneous rate of change of y = 3" at r = 0. Show your…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: First find gradient and take magnitude for max rate of change

Q: Find the rate of the change of the function f(x)=-cscx-sinx

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Q: Use logarithmic depreciation to find the derivative of y with respect to x

A: Given,  y = x7x+4   We have to derivative of y with respect to x

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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Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

A: