(a) Use the defin this section to fim f'(x) = (b) Find the insta

Q: If f(x) = 5x² – 2e*, find f '(x).

A: Given that  f(x) = 5x2 - 2ex  We need to find f'(x) and f"(x) . Now , f(x) = 5x2 - 2ex  So,   f'(x)…

Q: find the derivative, show all work please. f(x)=square root(4x2-2x+3)

A:

Q: Find the derivative of the 1 f(x) = x5 + (x² + 7)(x² – x – 2) + 17 5.

A: Given: fx=15x5+x2+7x2-x-2+17

Q: Differentiate the function. h(t) = √t-8e* h'(t)

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Q: Find f"(x). f(x) = (x? +7) °

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Q: =[in(4-x cos (r4

A:

Q: For the function f(x) =-X find f"(X), f"(0), f’"(1), and f"(- 1). "(X) = O I7

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Q: Let f(x) = r - 3z2 - 1. Calculate the derivative

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Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: What is f’(2) for the function attached below?

A: We have to calculate the derivative of the given function at x=2 f'(2)…

Q: Can you simplify for the f'(x) like the instructions says

A: The derivative is: f'x=5x51x+lnx25x4

Q: a. A(x) = 2tdt b. A(x) = f*₂2tdt

A:

Q: Let f(x) = square root ( 4x + (3x -5)10 ).Find the equation of the tangent line to the graph of the…

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Q: 3. Let f (x) = (3x2 + 1)?. Find f'(x)in 3 different ways by following the instructions below in…

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Q: 5 sec(x) f(x) = %3D 9(1 + 5 tan(x))

A: Formula:  Sec2x = 1+ tan2x d/dx (tan x) = sec2x

Q: Use the graph of f(x) to find the interval where f"(x) > 0. O A. (0,00) O B. (0,3) OC. (-3,00) O D.…

A: We need to find interval where f''(x) will be positive.

Q: C. A(x) = sintdt d. A(x) = ₁ It-2 |dt

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Q: 5л? + 3х — 14 (а) f(*) %3D 5х — 4 6x² + 4/x (b) f(x) = %3D

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.