Q2/ A) Use the definition of the derivative to find f(x) where f(x)=v3x+1

Q: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: Differentiate the functions. Find the derivative of y with respect to x. Use the given relation…

A: Given : Function y = x3 + 12   To find : Derivative of the given function dydx?

Q: Find the derivative of f(x) = (-x³ - 2x² - 2x) sin(x). Do not include "f'(x) =" in your answer.…

A: Topic = Derivative

Q: 1. Using the First Derivative Test, explain why the function f(x) =-2x has no extrema on any open…

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Q: Find the derivative of 1 f(x) || 1+ Vx using the definition of derivative. State the domain of the…

A: We have to find the derivative of the given function by using the definition of derivative.

Q: derivative of f(x)= 1/(x^2+5) is

A: Given,          fx=1x2+5

Q: Using either limit definition of a derivative at a point, determine the equation of the tangent line…

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Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

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Q: Using the definition of derivative, show that f'(2) = for f (x) = Vx+ 2.

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: Differentiate the function with respect to x using the chain rule to find f'(x). According to the…

Q: Find the derivative of the transcendental function. h(x) = - 14 sec x X h'(x) = -5x2-14 secx-tanx

A: We need to find the derivative of the given transcendental function.               hx=5x-14secx

Q: Find the x value(s) of any relative extrema. Use the Second Derivative Test to verify. f(x) = -x3 +…

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. f(x) =…

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Q: What rule must be applied in finding the derivative of f(x) = (3x^3-2x +1) (2x -3) * O…

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Q: 3. Use the limit definition of the derivative to find the equation of the tangent line to the curve…

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Q: ABANATUAN CITY B. Compute the derivative function f using the definition of the derivative. Show…

A: Using definition of derivatives.

Q: oFind the derivative: (show all 1. f(x) = 2xe-3x chou

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable.

A: The above problem belongs to the calculus part in which the topic is maxima and minima, the given…

Q: Use the definition of derivative (do NOT use the short cut method) to find f'(x) given that f(x) =…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: using the derivative definition how do I find f(x) = -6(square root over x).

A: The limit definition is on the board . First we find f(x+h) amd substitute the value in the limit…

Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: we have to find the second derivative of the function at the given point. f(x) = cos x2 , (0, 1)

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: Given function is fx=1x+4. Compute the first derivative. f'x=1x+4'=-12x+432

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

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Q: Find the derivative of f(x) = x² + 3x – 5 -

A: From the limit definition of derivative, f'(x)=limh→0f(x+h)-f(x)h

Q: Prove, using the definition of derivative, that if f(x) = cos x then f ' (x) = - sin x

A: we have to prove by using the definition of derivative that if f(x)=cosx then f'(x)=-sinx   as we…

Q: Using the limit definition of derivative, find the derivative of the function f (x) = 3x + 5.

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Q: find the derivative of f(x) = (x²+4)(3x³ – 2x) at the point x = - 3[ use product rule] В I !!

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Q: 3) Use the definition of derivative (do NOT use the short cut method) to find_ƒ'(x) given that f(x)…

A: This question is based on finding slope using definition of derivative.

Q: 2. Determine the derivative of f(x) = sin-'(2x)

A: Topic = Derivative

Q: How do you find the derivative of f(x)= sec(x)tan(x)?

A: Some properties of derivatives:Following are some of general derivatives and derivatives of…

Q: find the derivative of the function f(x) = x2 what is f'(3)? what is the equation of the line…

A: Given function is f(x)=x2

Q: 4 3. Лх) — Зх - 5 %3D

A: Given that  f(x)=4/(3x-5)^2  To find the derivative of f(x)

Q: se the limit definition of the derivative to find the slope of the tangent line to the curve f ( x )…

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Q: Using method of sub., find the Anti-derivative 1 x In x

A: detailed solution is given below

Q: 2. Using the definition of derivative, prove the following: (a) f)=- if fo)-V

A: Find the attachment

Q: Find the derivative of f(x) = (-x3 - 2x² - 2x) sin (x). Do not include "f'(x) =" in your answer.…

A: The given function is: fx=-x3-2x2-2xsinx   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: Use the limit definition of the derivative to calculate the derivative of f f'(x) = f(x)=-3x³ - 2x +…

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Q: f(x)=sinxcosx

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Q: Evaluate the derivative of the given function for the given value of x. Show all work.

A: Use the power rule and chain rule and quotient rule of derivative:

Q: Use the fact that the derivative of the function f(x) = is f'(x) = - to find the equation of the…

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Q: How do you find the derivative of f(x)=5/1-8x using the definition of a derivative?

A: The given function is f(x)=51-8x

Q: Use the definition of derivative to find f '(x) given that f(x) = 2x-5x +3 (do NOT use the shortcut…

A: The definition of derivative of f(x) is given by Given,  applying the definition of derivative we…

Q: Calculate the derivative for f(x) = (x+5)(x-1)(x-8). (Use symbolic notaion and fractions where…

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Q: Use the second derivative test to find the extreme values of the function f(z) = z-3z2-24z

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Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Given :   f(x)=x4 , at x=3/2 f(x)=1/4 , at x=2

Q: The derivative of a function is f '(x) = x2(x + 4). At what value(s) of x does f have a horizontal…

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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: