Choose the letter(s) of the correct answer. Choose E if none of the choices corresponds to the correct answer. Suppose f (x) is the integrand and F(x) + c is the antiderivative. How can one check if the answer obtained from integration is correct? A. Use differentiation such that F'(x) + c is equal to f(x). B. Differentiate F(x) + c and check if the answer is f (x)dx. c. Solve for f'(x) and it should be equal to F(x) + c. D. If and only if F(x) + c exists at all domain of f (x).

Q: = 5x² + 3x + xy = 5 and y(5): = 27, find y' (5) by implicit differentiation.

A: Given query is to find the derivative at indicated point.

Q: A non-exact equation can be converted to an exact equation by OA. Multiplying with the Integration…

A: Choose the correct option:

Q: Consider the function Compute f"(x). X = 66²⁰ - f(x) = -3t²- f"(x) = -4t+ 3 dt.

A:

Q: f"(x) = 24x2 + 2x + 8, f(1) = 2, f'(1) = -2 f(x) =

A: given that f"x=24x2+2x+8, f(1)=2 and f'1=-2 find f(x)

Q: . If f(x) = V4x – 7, find f'(x).

A: we have ;  f(x)=4x-7;  we have to find f-1(x)

Q: When z = f(x,y), which of the following is true for the whole statement? O ddz = f"(x).dx² and dx2…

A:

Q: F = If SF · dr = (5x − 3y²) dx + (x³y) dy, what is F?

A:

Q: m'+4m (1-m*)7

A:

Q: Find an antiderivative of (3x3+9x5)/x6 in the variable x where x does not equal 0.

A: From the given problem:   3x3+9x5x6   So,    3x3+9x5x6=∫3x3+9x5x6dx   We can simply write as:…

Q: Choose True if the statement is correct, otherwise False. If f(x)dx is to be integrated and u =…

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Q: On a test, a student makes this statement: "The functi f(x) = x² has a unique antiderivative." Is…

A:

Q: Let f'(x) = x*+4x³ + 2x² + 12x+1. a. For what values of x is f(x) concave up? (Blank 1) b. For what…

A: The given first derivative function is

Q: Find f'(1) for f(x) = In(v6x – 3).

A:

Q: Differentiate the functions. a) f(x) = 2 – 3x + b) f(x) %3D Зе* + sinx c) f(x) = 3x

A: As per guidelines, we will solve only first three subparts. Kindly repost other subparts separately.

Q: What is the anti-differentiation rule to be used in order to integrate the function f Vx5 dx. a.…

A:

Q: Find f. 13 f"(x)=x³+ sinhx, f(0) = 4, ƒ(2)= 5

A:

Q: 1 f (x) = x4 – Vx³ + x$

A: The function is given by fx = x4-x3+x18 To evaluate: The derivative of the function.

Q: Suppose that x and y are related by the equation 5x2−3y2=4 and use implicit differentiation to…

A: The equation is given by 5x2-3y2 = 4                                      ..........(1) To evaluate…

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: