Consider the function f (x) = 2x2 – 3x + 5. Construct the formula for the average rate of change function r = ARC, (x) and use algebra to sımplify your answer as much as possible. df Use the simplified formula from Part (a) to determine the formula for You must employ dx the definition of the derivative as a limit of average rate of change functions.

Q: Use the fact that e4x = (ex)4 to find d/dx(e4x). Simplify the derivative as much as possible.

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Q: g(x) = %3D I+3 32C

A: Derivatives

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Q: Find the derivative of the function. g(x) = ex³ - 2x g'(x) =

A: The function is given by gx = ex5-2x Formula Used: The chain rule of the derivative is ddxfgx =…

Q: Но Homework: Find the derivative of the function. x² y = x³ – X. +32x+3 40 y' = D %3D

A: We're going to solve

Q: Exercise To Try 13 Find using implicit differentiation, of 2x³ – xy³ = 3. NOTE: You will use product…

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Q: Find the derivative of f(x) = √5 - 4x. To enter √a, type sqrt(a). f (2)

A: The objective objective is to find f'(x).

Q: please show ALL your steps

A: we are given a function

Q: Determine the relative extrema using the Second derivative test. Find the point of inflection www y…

A: Let the function be, y=x(x2-5)2 Find the critical points using dydx=0 dydx=x2(x2-5)×2x+(x2-5)2…

Q: Let f (x) = x3 – 5x + 2, Use Derivative Rules to find the following: a) Find the equation of the…

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Q: b. f(x)=7x²e"

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Q: The equation that describes the volume of the conical shape RELATES the quantities : volume, radius…

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Q: Find the derivative of f (w) = 7ln (w) + 18.

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Q: Find the derivative y = (2x – a) (x² + e-")

A: We havey= (2x-x3)(x2 + e-x)

Q: (2) Define: F(x)=√(r² + 1). e³r+² dr. (a) Use the fundamental theorem (II) to find the derivative…

A: The given integral equation is:F(x)=∫x0 r2+1 ·e3r+2 dr

Q: use the reciprocal rule or the quotient rule to determine the derivative of the function.…

A: Given :Bu=u2u+1To find the derivative of the above function using reciprocal rule or quotient rule.

Q: 4. y=ysin 2xcos 5x + 3

A: Find your answer below

Q: Integrate each of the following functions with respect to x: (a) x⁹, (b)x¹/2, (c) x-³, (d) 1/x4, (e)…

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Q: exfex=6x²8h

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Q: TASK: The derivative of the function x?y? = x2 + y² is equal to y(1-y²) x(x² -1) TRUE or FALSE?…

A: Let's find.

Q: Differentiate the function L(x) = -6e"(cscx + 7cotx). Answer L'(x) =

A: Given Equation : L(x)=−6ex(csc(x)+7cot(x))   L'(x)= derivative of L(x)

Q: 2v f(v) = 2 - %3D 3

A: f(v) = 2 - 2v/3 We know that if, f(v) = vn Then, f'(v) = nvn-1

Q: y = 2x² - 8x. Determine the slope of the tangent to the function at x = 2.

A: To find the derivative of the function y=2x2-8xusing first principles,we start by using the…

Q: Find the derivative of the function.

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Q: Differentiate the function. y = (4x-2)5 (5-x³) 5

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Q: Vx+1(2-x)5 8) y = (x+3)7 Find the derivative

A: We have to solve

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: