The derivative of the function Is equal to Select one: a. e"(2" In 2 + 1) b. æ(2" In 2 + 1) c. e2²+= (2² In 2 + 1) de, "(2" In 2)

Q: Use the definition of the derivative to find f' (x) for f (x) = v2x + 1.

A: The derivative of f(x)=2x+1 is to be found using the definition of derivative. The derivative of…

Q: Find the derivative of function defined as follows.

A: we have to find the derivative of the given function . y=2x7-8x

Q: Find the second derivative of the function. Fx) = x In VR) + 9x f"(x) -

A: Answer and explanation is given below...

Q: Find the value of the derivative (if it exists) at the indicated extremum. -4 4/6 3 f(x) = - 3xVx +…

A: To find: The value of the derivative fx=-3xx+2. Formula used: Product rule of differentiation:…

Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

Q: Find the derivative of the following function. + 2x +x -5 -- 2 8 y 3x y' =D

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Q: Calculate the derivative indicated. f (4)(1), f (x) = x4

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Q: The degree of the derivative of f(x) = (3–x)'(x – 12)° is

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Q: Find the derivative of the function f(x) = In(2a? + 5æ)

A: ddxln (x)=1xddxxn= n xn-1

Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

A: Product Rule of differentiation : d(u.v)dx = udvdx+dudxv. dxndx=n.xn-1

Q: Find the second derivative for the functions defined as follows ƒ(x) = (x2 - 1)2

A: Given function: fx=x2-12 fx=x4-2x2+1 Differentiate the equation w.r.t "x"…

Q: Use the definition to compute the derivative of the function f (x) = Vx2 + 1.

A: We have to find derivative

Q: Which among the following functions has the derivative of de = (9z - 452 + 272) ( - 2) + (= - 2)*…

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Q: Find the anti-derivative for each function when C equals zero. 

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Q: Use the definition of derivative to a) f(x) = x - 2r? b) f(- %3D

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Q: calculate the derivative indicated. f (4)(1), f (x) = x4

A: Given: fx=x4 To find: f41 Solution: Power rule of differentiation states that: ddxxn=nxn-1 Finding…

Q: Use the definition of the derivative to find f fx) = 2/(x + 3)

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Q: Use the definition of the derivative to compute f'(x) given -4 fCx) f(x)= 3x-1

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Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=2 and f'(0)=3, what…

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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 following derivative if f(x) = x*. f(4)(2) = %3D

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Q: The derivative of the function f(x) = 3* is 3* Select one: True False

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Q: Use the definition of the derivative to differentiate the following function. 1 f(x) = x² – 2 -

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Q: Evaluate the first derivative of the function below at (1, -2). 3x4y² - 7xy³ = 4 - 8y

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Q: Use the formal definition to find the derivative of f(x) = 4 at x = 8. x+3

A: To find the derivative of the function  f(x)=4x+3 at x=8

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

A: Proceed as shown below

Q: Use the definition of the derivative, to find the derivative of y (x) x +1 x + 4 (x + 4) 1 (x + 4) 3…

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Q: The derivative of the function is equal to

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Q: By using the definition of the derivative find to f "(x) 3x3 +1 1 Ve +1 x +1

A: 1. We solve first order derivative of f(x)

Q: a)f(x)=3* b) gu) =7-x

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Q: f(x) = (x+3)*(5x+1)* (3x² – 4) 11.

A: According to guidelines we should have been able to solve only first question at a time #11

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

A: Considering f(x) = 9 – 5x. To find the approximate derivative of f(x) at x = 2.

Q: Find the second derivative of the following function: f(x) = esin1, %3D

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Q: f (x) = 5x* f(x) %3D 12x5—4х4

A:

Q: Find the given higher-order derivative. f(3)(x) = /x5, f(4)(x) f (4)(x) =

A: Given,f3(x) =x56d3f(x)dx3= x56 = z(say)We have to finddzdx= d(d3f(x)dx3)dx = d4f(x)dx4 = f4(x)

Q: Which of the following is the derivative of g(x) =x'Inx?

A:

Q: -1

A: Integration of given function

Q: Find the derivative of the function below: 4 f(x) + 1600 In(3 x7 x8 f'(x)

A: Given : fx = -4x7-5x8-6x9 + 1600ln3

Q: State the formula for the definition of the derivative of a function f (x) provided x is any number…

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Q: use the definition of the derivative to compute f'(x) given f(x) 3x+2

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Q: Evaluate the second derivative of the function below at (1, -2). y² = x³ = x + 1 -

A: To evaluate the second derivative of the function at the given point.

Q: f(x) = Vx2 + 5x-

A: We have given the function;

Q: Find the given higher-order derivative. F(3)(x) = Vx5, f(4)(x) f(4)(x) =|

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Q: By using the definition of the derivative find to f'(x) 3. 3x

A: our objective is find the derivative

Q: The derivative of the function ein(10) is equal to

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Q: Which is the derivative of f(5x)

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Q: 2. Use the definition of the derivative of a function at a number to calculate f'(8) where f(x) is…

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Q: Suppose f(x) = x^2−3x−5. Using the definition of derivative, compute f'(3).

A: Consider the given function: Here the objective is to find the derivative of the given function…

Q: Find the higher order derivatives for f (x)=x^5, what is f^(6) (x)?

A: According to the given information f(x) = x5 and it is needed to calculate f6(x).Since, if p(x) is a…

Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

A:

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: