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

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

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A:

Q: Find the derivative by the limit process. x) = 11 -x

A: Given, f(x)=11-x2

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A: fx = 342-x

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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

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A: given function f(x)=4/x we have to find a) the the derivative of f(x) at x=2 using the limit…

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A: We have given function  f(x)= x2 So using definition of derivative  f'(x) = limh→0fx+h-fxh So,…

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 fx=6xddxfx=limh→0fx+h-fxh

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A:

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A: Please see the below picture for detailed solution.

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

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Q: Find. the derivative of tan(x)). with respect to X 1- y3=

A: Explanation of the answer is as follows

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A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

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A:

Q: By using the limit definition of a derivative, determine the derivative of f(x) = 1/x at x  = 2

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A:

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A:

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

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

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

Q: find the derivative of y with respect to x, t, orθ, as appropriate.

A: On simplification, we get

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A:

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A: To prove the given limit

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A: On solving this we will get

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

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A: Explanation of the answer is as follows

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A: Consider the provided function y=arctan(x).

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

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A:

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Q: 1 m' (x) = x In(x)

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A: The derivative of the function is defined by,

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A:

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

A:

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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: