Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 4 +Ex2 - 5 6 F(x) =

Q: B) Find the third derivative of the function: Y = + VX3 %3D

A: We have to find third derivative

Q: Find the derivative of the function. F(t) = e4tsin(2t)

A: Find the derivative

Q: Find a formula for df 1 dx for the function below using the Derivative Rule for Inverses. f(x) = (5…

A: Given,         fx=5-3x3We know that,           The Derivative Rule for inverses is given by…

Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

A:

Q: r(s) = V2x² + 3x – 1 %3D

A:

Q: What is the first derivative with respect to x of f(x) = (x² – 4) (3x – 2)? a. (2x)(3) b. 6х (x + 2)…

A:

Q: a. y = x? – x + 1| 1 b. f (x) = 2x+1

A: We have two equations as a function of x . Hence we can differentiate both the equations with…

Q: Find the derivative of the function y = √(e2x + e−2x)

A:

Q: nd the derivative of the following function with respect to x. V5x + 8 V1– 9 cos (4x) Vx² + 10x h…

A:

Q: Find the derivative of the given function. y= 2x°-8x +16x+4 dx II

A:

Q: If f(x) = 6x²e*, then what is the derivative of f(x) with respect to x? 6xex O 12xe* О бхе"(x + 1) O…

A:

Q: Find the antiderivative for each function when C equals 0. Check your answers by differentiation.…

A:

Q: Find the derivative of the function. 1 + e5x e 5x 3x e

A:

Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: 3. Find the derivative of the following functions using differentiation rules. x2+V+V+14 a. y = b. y…

A: In order to solve the given problem use product quotient rule of differentiation in part(a) and (c).…

Q: 2. Is the function G(x) = 2e -5 an antiderivative of the function g(x) = 6e"? Use the…

A: Given information: function Gx=2e3x-5 function gx=6e3x here, we have to show that, the function G(x)…

Q: If f(x) = eX, then what is the derivative of f(x) with respect to x? %3! O 7e7x O e'*(x + 7) O…

A:

Q: Given that h(x) = xi + what is the anti-derivative of h(x)? (Do not include the constant C'in your…

A: Anti-derivative

Q: Q. / Find the derivative of y = (In(x²))'n(x²).

A:

Q: e Find the derivative of the function g(x) = 2+ 3x g'(x) =

A: See solution below

Q: Find the derivative of the function.

A:

Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Given  C'x = 3x2-6x;  C0=3,000.

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A: Explanation: The given function is: f(x)=-3xx+1 Find the first derivative of this function.…

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A:

Q: Using implicit differentiation, find dæ2 in terms of æ and y, given that z+y + 6x = 1. dæ²

A:

Q: d By using the definition of the derivative, find the for: dx f(x) = Vx

A:

Q: Determine the value of the derivative of the function stated below, at x = 1. d "2х-1 4 dx \ x+2

A: The given function is: f(x)=2x-1x+24

Q: 2) Find the derivative of the function. T(r) = ar² + 2e" + n². %3D

A:

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Given  C'x=2x2-3x   ...1C0=4000   ......2

Q: For what value/s of x is the derivative of the function - Vx² + V¤ equal to 1? O x= 1/27 O x = -1 O…

A: Consider the given function -x23+x3.   Obtain the derivative as follows. ddx-x23+x3=-23x-13+13x-23…

Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

A:

Q: Ax) = Vã Vx = /x хх e

A:

Q: C) Find the derivative of y= (1+ x²)*

A:

Q: Find by implicit differentiation. dx 1. x3 – xy + y? = 7 2. x³y + y?x = -3 3. xy = x?y + 1

A:

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: Find the derivative of the function g(x)=(3x^2+2x+4)e^x

A: Given that: g(x)=(3x2+2x+4)ex

Q: Using the definition of a derivative, find t'(3) given t(1) =2 -9z-1 %3D

A:

Q: Find the derivative of the function. f(x) = (7 − e−2x)6   f '(x) =

A: To determine the derivative of the function.

Q: Find the derivative of the function. Q(x) = V e8x + x %3D Q'(x) = %3D

A:

Q: Find the derivative of the function. -Vx? y = + 36 6 + Vx2 + 36 1 In 36 6x2

A:

Q: The third derivative of y=x is A) 0 B c) None of the given choices D) 6x E) 3x

A:

Q: 3. Given x?y? = x² + y², find by implicit differentiation. dx

A: To find: The value of dydx. Given: The equation is x2y2=x2+y2. Formula used: Product rule of…

Q: с. у %3D (3х — 1)(2х + 5) d. g (x) — х3 — зЗx2 + 2

A: Product rule of differentiation: ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x) Power rule of differentiation:…

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

A:

Q: Find the second derivative of the function. f(t) = t?e-5t f"(t)

A:

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Solution: C′(x)=3x2 −5x​; C(0)=2,000

Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

A:

Q: 2. f(x) = 2x – 5x%

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: