13. In y = what is the derivative of 2x2 +3? x+1 a) 2x b) 4x c) 4x +3 d) 7

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: The tangent line equation of 2x6+y4=9xy at the point (1, 2) is ….

A: The tangent line equation of 2x6+y4=9xy

Q: Use the sign of the derivative to establish the inequaltiy In(1+x) > I -,V> 0. 2

A: See the attachment

Q: Find the derivative. y= In x+3 %3D

A:

Q: Find the third derivative of y = (6x - 1). Show your %3D in negative exponent.

A:

Q: - Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A:

Q: Estimate the second derivative of f (x) = difference approach with h=O.1? 25x3 6x2 + 7x -88 at x-2,…

A:

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

A:

Q: Find the derivatives of the functions in Exercis

A: We need to find the derivative of the function, y=5-2x-3+182x+14

Q: 1. у %3D 4x? — Зх — 2.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: What is the relative error in estimating the first derivative of f (z) = 25x - 6x2 + 7x- 88 at x-2,…

A: Given equation is f(x) = 25x3 - 6x2 + 7x - 88∴ f′(x) = 75x2 - 12x + 7

Q: Compute the second derivative with respect to x of 3x3 + 8 y = at x = 1.

A:

Q: What is the gradient of the tangent line to the curve y = 2x³ – 3x2 at the point with a = 2? |…

A:

Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z - 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: 5) What is the equation of the line tangent to y = 2x³ + 3x - 1 atx=0?

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan x y =…

A: According to the Fundamental Theorem of Calculus, If gx=∫axftdt , then g'x=fx Consider the given…

Q: 1. у %3D 4x2 — 3х — 2.

A:

Q: Find the equation of the tangent line of funclion y= ²+1 23 -2 at (40,- 73)

A:

Q: Find the derivative of f(z) = 3+ 2x² – 2y² + i4xy .

A: We find out the derivative of given function .we differentiate both sides with respect to z and take…

Q: ) Find the derivative of y = [7 cos5(5x – 8)(cos³V2x – 1)] %3D

A:

Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

A:

Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

A: We have to verify that given statement.

Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the derivative using Implicit differen tiation 3 %3D 3xy? 2

A: Given: x3+y3=3xy2 We have to differentiate above equation using implicit differentiation. In…

Q: Find the derivativeof the following function:

A: To determine derivative of the function.

Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

A:

Q: 3/ By using the definition of derivative, proof that tan x = sec? x. %3D dx

A: By definition of derivative , f'(x) = d(f(x)dx= limh→0f(x+h) - f(x)h L Hosital's Rule :When limit is…

Q: 3. Find the slope of the line tangent to f(x) = In(4x² – 3) at (1,1).

A:

Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

Q: Compute the derivative of g(æ) = e dt. 22 -2xe -2xe O -2re

A:

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: What is the derivative of cy = 2 - a°y ?

A:

Q: Find the second derivative by implicit differentiation of 8x2 + 16y2 = 144 at (1, 1)  Choices: A.…

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

A:

Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

A:

Q: What is the derivative of y = etan-1 2x 2

A:

Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)

A:

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A:

Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

A:

Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: . The derivative of y = 3VX4 – cosx is - D. x*/3 + cosx A. x/3 + sinx В. 4х /з + sinx C. 4x*/3 +…

A: y=3x43-cosx⇒y=3x43-cosxThen dydx=(3×43×x43-1)-(-sinx)                           =4x13+sinx