3 b) Determine the derivative of - from First Principle. (5)

Q: y = In (x* + 5)³

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Q: Explain how to apply the First Derivative Test.

A: Explain how to apply the First Derivative Test.

Q: 1. When an object is in free fall near the surface of the Earth, the only force acting on it is the…

A:

Q: Compute the derivative of the function y = 5 sin-'(x) at the point x = (Use symbolic notation and…

A:

Q: Using Leibnitz theorem, the nth derivative of xy, is

A: We have to find nth derivative of xy1 using Leibnitz theorem.

Q: Use Leibniz’s Rule to find the derivatives of the functions

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Q: What is the derivative of ex? What does it mean that the derivative is equal to the value of the…

A: Explanation of the solution is given below...

Q: 5. Find the second derivative of * sin- (æ?)

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Q: What are the the mean value theorem in application of derivatives?

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Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

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Q: Compute the derivative using derivative rules that have been introduced so far. y = (x 4 + 5)3

A: Given equation is y=x4+53 Applying derivative with respect to x: dydx=dx4+53dx Using the power rule…

Q: Determine the local optima of the following functions using both the First derivative test and…

A: First derivative test: let f be a continuous on [a,b] let c be a critical number for f in (a,b).…

Q: 2. If the derivative of an accurately determined function is replaced with a finite difference, how…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: What are application of 1st principle method of derivative?

A: First principle method: Differentiation from first principles: Given a function y=f(x) its first…

Q: Find the points on the graph of f where the tangent line is horizontal. tangent line is 3x^2-16…

A: The tangent line is horizontal where y'=0

Q: Estimate the derivative of the following using simple and high-accuracy backward, forward and center…

A: Similarly, calculate the function for h = 0.05

Q: Compute the derivative of the function y = 7 sin¬'(x) at the point x = (Use symbolic notation and…

A: A detailed solution is given below

Q: 3. Calculate the derivative of f (x) = x2 +1 showing all your work.

A: Using the formula u by v = vd/DX(u)-u d/DX(v)/v^2 According to the bartleby guidelines I can  solve…

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: On which derivative rule is the Substitution Rule based?

A:

Q: State the Second Derivative Test

A: Second Derivative Test:   This is used to find local extrema.

Q: 23. The slope of the tangent line indicates the rate of change of the function, also called the 24.…

A: Since, you have asked multiple question, we will solved the first question for you. If you want any…

Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

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Q: Calculate the derivative.

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Compute the derivative of the function f(x) = 5x² + 3x at the point x = 4. %3D (Give your answer as…

A: We have to find the derivative at that point

Q: 2. Identify the derivative (9) based on the product rule ie, (G). Simplify to a single term.

A: Given ∂∂TGT

Q: Find the derivative fex=exV3x+2

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Q: Compute the derivative of f(x)= (ex2 +e-x2 )/(ex2 -e-x2 )

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Q: 3. Find the derivative of f (x) tan (5x + 7), by first principle of differentiation

A: Given function is By first principle of differentiation, we have

Q: (5) Match the graphs of the functions to the graphs of their second derivatives. Original Functions…

A: Given: a function their derivative.

Q: 28 dt dz -1

A:

Q: How do I find the derivative of this problem?

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Q: Compute the derivative of the function y = 8 sin-(x) at the point x = (Use symbolic notation and…

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Q: Derive a formula that approximates the second derivative of the function sampled at x = 0, 0.01,…

A: Let us assume that second derivative function  f"x0=Afx0+Bfx0-h+Cfx0+2h can be rewritten as…

Q: What is the value of the second derivative y" at the point (4,3)

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Q: 2. Use an example to show how to use the First Derivative Test for critical points

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Q: Calculate first, second, and third derivative values for function, f(x) = -x2 + 5x + 3 at points x =…

A: Forward difference Consider a linear interpolation between the current data value (t0,I0) and the…

Q: A derivative in Leibniz notation is written as a fraction of differentials. A True B) False

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

Q: 9) Find the value of the derivative at the point (2,-18) ƒ(x) = -3xV2x + 5

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Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: On which open interval is the derivative positive/ negative .

A: Given:

Q: Can the  derivative of f(x) be zero in the interval [-1,0]

A: Given, fx = x4+8x+3  f'x = 4x3+3   We have to find the derivative of fx be zero in the interval -1,0…

Q: 3. Estimate the derivative using forward finite divided difference applying both truncated and more…

A: Given f(x)=12+xe2x To find the f'0.5 at h1=0.25 and h2=0.125 using forward finite divided difference…

Q: Find the derivative of the function at Po in the direction of A. f(xу) 3 - ху- Зу?, Po(-7,0),…

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Q: 9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7

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Q: Find the derivative of using first principle?

A: we have to find first derivative of y by using first princple

Q: 4 Find the derivative of f(x) using first principle %3D 3x2-3 of differentiation.

A: