Use the definition of the derivative to determine whether x < 0 0 < x < 1 1 < x < 2 (10x2 + 41, x > 2 x, f(x) = is differentiable at x = 2. x2 + 5,

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: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

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Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

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

A: We have to find f'(x)

Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: Use the alternative form of the derivative to find the derivative at x=c ( if it exists). f(x) =…

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Q: Find the critical points of the following function. f(x) = 5x? - 3x – 1 What is the derivative of…

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Q: Find the derivative of the function 3 f(x) = V (x² – 2)' at x = -1. f'(- 1) =

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Q: Use the alternative form of the derivative to find the derivative at x=c (If it exists)…

A: Given function is fx=x3+3x2+9. We know that, f'x=limx→cfx-fcx-c Given c=-3 Therefore,…

Q: What is the derivative of f(x) = - 3 with respect to r? %3D

A: Given: The function f(x)=-3x3

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Given that f(x)=x2-9 , c=8 find the derivative at x=c by using alternate form of derivative

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

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Q: Use the alternative form of the derivative to find the derivative at x = c  (if it exists). f(x) =…

A: Definition used -           Alternative form of derivative -…

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: FIND THE DERIVATIVE OF THE GIVEN 4.) f(x) = sec x ニ 5.) y= In「3-2メ |- 3x 6.) y= Inle-*+ xe-*)

A: 4. To find: The derivative of the function. Given: The function is secx. Calculation: Use the chain…

Q: Find the derivative with respect to x of 1 f(x) V3x + 9

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Q: Find the derivative of the function f(x) = x2 - 5x + 3 at the numbers (a) 2 and (b) a. %3D

A: a. From the definition we have the following, Simplify further,

Q: Use the alternate form of the derivative to find the derivative at x=c, if it exists. f(x) = x³ +…

A: Given f(x) = x³ + 2x² + 1, c = -2 Find the derivative at x= c if exist by using the alternate form…

Q: Find the derivative of the function. (x) = In(4 – x®) r"(x) =

A: We have to find

Q: Find the derivative of the function. r(x) = In(x + 1) + 5x7ex r'(x) =

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: find the derivative of f (x) at the designated value of x. f (x) = x + 11 at x = 0

A: To find the derivative of f(x)=x+11 at x=0 Solution: f(x)=x+11 Differentiating both sides w.r.t x we…

Q: By considering the derivative of the function f : [-1,-1] → R defined by f(x) %3D r2 – x+1' 3. show…

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Q: Use the definition of the derivative to show that the derivative of y = f(x)3 2/ is 1 f'(z) = VI %3D

A: GIVEN f(x) = 2√ x CALCULATE f'(x) = 1/ √ x

Q: Use the fact that the derivative of the function ​f(x)=4/x is f"(x)=-4/x2 to find the equation of…

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Q: Calculate the derivative of the function below using the quotient rule. x4 y = Vx + 2x4 f(x) = and…

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Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

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Q: Use the limit DEFINITION OF A DERIVATIVE to find the derivative of the function. 16) f(x) = Vx + 5…

A: The derivative of a function y=f(x) is given by f'x=limh→0fx+h-fxh. The given function is fx=x+5.

Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: To find the derivative at x=c of f(x).

Q: Use the definition to find the derivative of the function f(x) = Vx +1 and obtain the equation of…

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: Use the definition of the derivative to find: f(x)= 1/x^3 g(z)= z^4 - 8z^2

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

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: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition

Q: Evaluate the derivative at the given value of x. 10) f(x) = x2 + 5x at x = 4 %3D

A: I did with limit definition of derivative

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

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Q: Show that f (x) = 1x-5| is NOT differentiable at 5 by using the definition of the derivative, (Start…

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Q: What is the derivative of f(x) = 1 over x⁵

A: here we use the formula of derivative  ddxxn=nxn-1

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Find the derivative off with respect to x of f(x) = In x⁹. The derivative off with respect to x of…

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