Calculate the derivative of f1 (x) = (2x + 3) / (x - 5) using the definition of the limit of the rate of variation.

Q: y = 4x° + 4x at (1, 2)

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Q: Find the derivative of the function by the limit process. f(x)= 2/x2

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Q: Find the derivative of the function by the limit process.

A: We have to find derivative of the function using limit process: fx=x+4 We know the formula of…

Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: Use the second-derivative test, if possible, to find relative extrema of y x5 – 5x. -

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Q: Compute the derivative using derivative rules that have been introduced so far. y = (x 4 + 5)3

A: Given equation is y=x4+53 Applying derivative with respect to x: dydx=dx4+53dx Using the power rule…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 7x +…

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

A: Given fx=6xddxfx=limh→0fx+h-fxh

Q: f(x)=x² -3x.

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Q: In(x²) What is the derivative of

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Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

Q: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: Use the limit definition of the derivative to find the instantaneous rate of change o ƒ(x) = 5x² +…

A: We have to find rate of change

Q: X-3

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Q: Find the derivative using the Four-step rule f(x)=x/1-x

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Q: 2. f(x) = x2– 5x + 6 at x 2 --

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x)=2x2+5x+3…

A: we have to find the instantaneous rate of change of f(x)=2x2+5x+3 at x=3 by  limit definition of the…

Q: Determine the derivative of y=(x−1)4 without using the power rule.

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Q: Find the derivative of function.

A: We have given y=-2ln x3x-1. Differentiate both sides with respect to x. Use constant multiple rule…

Q: Find the derivative of the function by the limit process.

A: The given function is fx=-5x. Obtain the derivative as follows.

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x)=6x2+2x+3…

A: The limit definition of derivative is given by: We know that f(x) = 6x^2 + 2x + 3  Now we will find…

Q: Find the derivative of the function by the limit process.

A: Consider the function, fx=12 The limit definition of the derivatives of a function is given by the…

Q: Find the derivative of the function by the limit process. f(x) = 5x − 4

A: fx=5x-4

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x² +…

A: From the limit definition the instantaneous rate of change at x=a is given by: f'a=limh→0fa+h-fah…

Q: Find the derivative of the function by the limit process.

A: Given: fx=x3-12x

Q: Find the derivative of the function by the limit process. f(x) = x2 − 5

A: Given function is By limit definition of the derivative

Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 3x + 5x…

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Q: Find the derivative of the function by the limit process. f(x) = 1/x2

A: Here the given function The first derivative of function f(x) is defined by limit prosses as

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x² +…

A: We will find the instantaneous rate of change of f(x) at x=4 as following.

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2-5 To Find: The derivative of the given function by the limit process

Q: Find the derivative of the function by the limit process. f(x) = x3 − 12x

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Q: find the derivative of the function f(x)=x^3+2x at -3

A: find the derivative of the function f(x)

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x +…

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Q: use the limit definition of a derivative to find the slope of the tangent line of the function…

A: Recall the limit definition to find the slope of the tangent line of the graph.

Q: Find the derivative of the function by the limit process. f(x) = vX +7

A: Given,          The function is fx=x+7.

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x +5x…

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Q: nd the derivative by the limit process (Gener x) = Vx2 - 4

A: In this question, the concept of the derivative is applied. Derivative The derivative is used to…

Q: Find the derivative of the function by the limit process. f(x) = 7

A: The given function f(x)=7. The derivative of the limit  for the function f(x) is defined by So, to…

Q: find the derivative by using the definition of a deriviative.f(x)= 1/3x+2

A: according to definition of derivative we will evaluate the 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 the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 4x2 + 4x…

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Q: Calculate the derivative of h(x)= square root of x+1 when x=8 using alternate difference quotient

A: derivative of h(x)= square root of x+1 when x=8 using alternate difference quotient

Q: Find the derivative of the function by the limit process. f(x) = x3 − 2x + 1

A: Given function is fx=x3-2x+1. From the definition of derivative, we have f'x=limh→0fx+h-fxh Using…

Q: Find the derivative of the function by the limit process. f(x) = −5x

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 7x² + 2x…

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Q: Estimate the derivative of the function f (x) =: -3 at the point a = 3.

A: The function is given by fx=x3-3 differentiate the above function w.r.t "x" f'x=ddxx3-3…

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

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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: