Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is the answer lim (2h/h) ≠ lim ((2/x+h) − (2/x) /h.                               h→1−                h→1+

Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: Determine the derivative of f(x) = 3 x2 In x with respect to x. f '(x) :

A: We differentiate both sides with respect to x and apply the rule d/dx(uv)=ud/dx(v)+vd/dx(u)

Q: 2. Use the definition = f'(x) = lim f(w)-f(x) to find the derivative of y = tan x. dx w-x

A: Let's take; w - x = h w = x + h As w approaches x; w-x = h →0   f'(x) = limh→0  [f(x+h) - f(x)]/(h)…

Q: Use the limit definition of the derivative to prove the following special case of the Product Rule:

A: The derivative of the function is the rate of change of the value of the function when the value of…

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

Q: Let f(x) x + 1 Use the limit definition of the derivative to find the slope of the line tangent to…

A:

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 7.

A:

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: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: Use the definition of derivative to prove that In(1 + x) lim 1

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Q: Find the derivative by using the definition f(x + h) – f(x) f'(x) = lim where f(x) = v4x +7 h+0

A: given                  f(x)=4x+7

Q: Find f'(a) using the definition of the derivative. if f(x) = Use the definition of %3D derivate…

A:

Q: Use the limit definition of the derivative to prove the following special case of the Quotient Rule:

A: We have to prove the following derivative by using limit definition: ddxfxx=x f'x-fxx2 We know for…

Q: Use the definition of a derivative to determine all points for the function f(x) = ((x+|x|)^2)+1 is…

A:

Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

A:

Q: find the derivative x using the of f (x) = x2 - definition of derivative, %3D f(x+h)-f(x) lim h0 h

A: Answer

Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Find the derivative of the following function using the limiting process. f(x) = 1/x2

A:

Q: fx て (X)

A:

Q: for f(x) = 3-x/2x+3 , find the f'(-1) using the limit definition of derivative. then use it to find…

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

Q: Let f(x) = √x. Find the derivative of f(x) at x = 2 by using the definition of the derivative as a…

A:

Q: Use the rules for derivatives to find the derivative of function defined as follows.

A: The given function is: y=ln2x-1x+3 To find the derivative of this function, apply the quotient rule,…

Q: Use the fact that the derivative of the function g(x)=√x is g"(x)=1/2√x to find the equation of the…

A:

Q: Find the derivative of function defined as follows. h(x) = (x2 - 1)3

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Q: Let y be a function of x and suppose y=In(x²+y²). What is the correct result for the derivative of y…

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Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

Q: use the definiton of a derivative to find the deriviative of f(x)=3x^2+x

A: we have to determine the derivative of f(x) using definition  of derivative .f(x) is given as below

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

A: we have to find the derivative

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 11.

A: Here we have to use limit definition to find derivative

Q: (0) x %3D 글*- St-3 5t – 3 2

A: Explanation of the answer is as follows

Q: .. Consider the quadratic function y = 4-x². Using the limit definition, ind the derivative of the…

A:

Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

A:

Q: Use the limit definition of derivative to find the slop of the tangent line of f(x)=5x^3+x at (1,6).

A: The derivative of the function is defined by,

Q: Use the limit definition of the derivative to prove the following special case of the Product Rule:…

A:

Q: Find the derivative of the given function using the limit definition f(x) = ;1 = %3D

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Q: The derivative of f with respect to x of f(x) = In x° is

A: Since, you have posted multiple questions. As per guidelines I"ll solve only first question. If you…

Q: Find the derivative of the following functions using the limit definition. 1. y = x² – 4x – 5 -

A:

Q: Use the limit definition of derivative to find r at the point c= 2.

A: The given function is fx=x5 ...(1). By using the limit definition of the derivative, the derivative…

Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: Use f'(x) = lim **n)=l to find the derivative at x for the given function. h h-0 s(x) = 8x +7 s'(x)…

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: Find the derivative of the transcendental function. h(x) = 7e cos x h'(x) = %3D

A:

Q: Suppose the derivative of the function y = f(x) is y' = (x-9)2(x+6). At what points, if any, does…

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Q: Find the derivative of f with respect to x of f(x) = In x'

A:

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve…

A:

Q: Find the derivative of the function y = 3x? – 4x + 7 using limit definition.

A: Given: y=3x2-4x+7

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: