Write the first and second derivatives of the function. 4.2 In x7.1 f(x) f'(x) f "(x)

Q: 1: Using the definition, calculate the derivative of the following function. S(x)=4-x²

A: Topic:- derivatives

Q: 5. Calculate the derivative of f(x) = Use this result to determine whether the sequ x2 + 1 an = n2.…

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Q: Question: What kinds of function behavior would result in the function f not having a derivative at…

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Q: 6. The graph y = f'(x) of the the derivative of a function f(x) is shown below. Answer the questions…

A: Given that: Graph of f(x)       NOTE: As per our answering guidelines, we can only answer 1 question…

Q: 3. Find the first and second derivatives of the function f (x) = e¬²

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Q: 9. [Essay] Find the derivative of y = 3x + 1). За* (x? — Зх + 1). Зах

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Q: Find the derivative of the following function. f(x)=ln(e2x+3) evaluated at X=ln 4 The value of…

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Q: 4. Determine the derivative of the function with respect to x. 8sin?(x² + 2) y = 4tan²(x² + 2)

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Q: 5х 6a) Find the derivative using logarithmic differentiation: y = (tan x )x

A: The function is given as y=tanx5x Taking log to the both sides logy=logtanx5xlogy=5xlogtanx…

Q: 8. Find the derivative of the following functions with respect to x by using either the product or…

A: Part (a):   Apply the product rule:

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Q: 2. Find the derivative of function y (y is a function of p). y = eP(p + PVp)

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Q: Without evaluating derivatives, which of the following functions have the same derivative: f (x) =…

A: Use the properties of lograthim and simplify the given functions than guess which have same…

Q: 10 Зх — 1 Find the derivative of the function F(x) = 2 – 3x Answer

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Q: 23. Find the derivative of the function. f(x) = 6sin?(-5x8) %3D f'(x) = %3D

A: Here is the solution of the given problem. Derivative: By chain rule

Q: The table below gives selected values for the differentiable and increasing function f and its…

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Q: Find the derivative of the algebraic function.

A: Given: f(x)=4-3x-x2x2-1

Q: 2. Find the derivative of the following functions: (a). f(x) = x + 4x-2 + 6e" [1 Mark]

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Q: 8. Evaluate the derivative of the function y with respect to x. y = 5*e*

A: This question is related to differentiation, We will solve it using given information.

Q: 6. Find the second derivative, f"(x). (6) = f(x)

A: To find  The second derivative of f(x).

Q: Find the derivative of the following functions: b). ?(?)=2tan^−1(?)−7?

A: To find the derivative of  y(x)=2tan-1(x)-7x

Q: (A) Find derivative of y = In V4+ a2

A: Given that a function y (x) and we find derivative of this. We know that : d(lnx)/dx = 1/x . Here i…

Q: - 5 then what is the derivative of y with respect to x?

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Q: (12) Find the derivative of the function Y = cos (a³ + x³)

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Q: Find the second derivative of h(x) = 6(?3 + 4)3

A: Solution : The objective is to find the second derivative of the given function

Q: (10) Use logarithmic differentiations to find the derivative of (За? — 2)5 (2x35)7(41)-11 y

A: The given function is

Q: 5e* Find the derivative of f (x) Зех+1

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Q: 2² – 6 Calculate the derivative function of g(x) Write your result as a single fraction. %3D 5а + 1…

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Q: 10.Use the definition of a derivative to the derivative of the following functions. x+3 f(x) 32x +5…

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Q: Use the DEFINITION OF A DERIVATIVE to find the derivative of the function. Worth 2 questions. 8 8)…

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Q: 2.) f (x) %3D х

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Q: Consider the following. x² f(x) = x + 7 Find the derivative of the function. f'(x) = x(x+14) (x+7)²…

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Q: 5. Find the second derivatives. f(x) = x cos(x) and g(x) =

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Q: 8. Find the derivative of the following functions with respect to x by using either the product or…

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Q: 5.) f (x) = 2x² – 3x – 5 Зх —

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Q: Find the derivative of the function.

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Q: Find the derivative of the following function. 2 ex -5 f(x) = 2 ex +5 (Type an exact answer.)

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Q: 3. Find the derivative of the following (a) f(r) = x" (b) f(r) = (2" + 1)in + 2" %3D

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Q: 3.) f (x) 3 5х — 3

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Q: 4. Find the second derivative of the function. Simplify if possible. f (1) = 2+5

A: topic - derivative

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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Q: Consider the second derivative function f" (x) = 3x² + 4x – 1. Find f (x) if fº (0) = 7 and f (0) =…

A: See the attachment.

Q: 8. Find f '(2) if f(x) = [g(x)]*, and g(x) = x + 2

A: g(x) = x+2  f(x) = [g(x)]4  f(x) = (x+2)4

Q: 100 1 The derivative of the function is equal ecos x to

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Q: III. Find the indicated derivative of the following. 1. x? -4y? =5 , y"

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Q: 4. The derivative of the function f(x) = r +3) is

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Q: 2. Using the definition of derivative, prove the following: 1 (a) f'(x) =E if f(x) = V

A: The given function is  f(x) = x1/3 To find f'(x)

Q: 2. f(x) = 2x – 5x%

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Q: Find f’ (x), i.e. the first derivative of the question below f (x) = (x - 4) (x – 1)

A: Topic:- derivatives