Let f(æ) = /8x. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim %3D enter the expression needed to find the derivative at a = 4. f'(4) = lim 4 After evaluating this limit, we see that f'(4) = Finally, the equation of the tangent line to f(æ) where a = 4 is

Q: Compute the derivative of the function y=arcsin1√x at x=2.

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A:

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

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A: We use the limit definition of the derivative

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A: We use the chain rule and product rule

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A:

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

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

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A: Given function is Differentiating both sides with respect to , we get

Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

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A: Soln:To find the derivative of sinh-1x

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A: Explanation of the answer is as follows

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 5s

A:

Q: Discuss the relationship between the derivative dy/dx and (Lim) with drawing if it is required ?

A: See the attachment

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A: We will prove the given statement.

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Q: Find the derivative of function.

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Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

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A: f(x) = 3-x2x+3using limit defination f'(-1) = limx→-1f(x) -f(-1)x+1…

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…

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A: See the attachment

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A: slope of the tangent line is m=dydx at (1,7)   By limit definition of…

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A: The given function is f(x)=4x2We have to find the derivative of f(x).

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A:

Q: 2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

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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

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A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

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

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A: Given:

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A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

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Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

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A: The given function is: y = sinh-1 (tan x) The derivative of y=sinh-1θ is: ddθsinh-1θ=11+θ2.

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A: To find the slope of the tangent we need dy/dx at x=2 So the slope of the tangent is 4

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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: