[1] Let f(x) = x – 4.x³ + 3.x² – 4x – 4. Find the equation of the tangent and normal line to the curve of f(x), where x = -1 and x = 2.

Q: Find the derivative of the following functions. 1. y = (6x² + 7x)* 2. g(t) = (41² – 3t + 2)2 3. y =…

A: Derivatives

Q: ind the derivative of the function f(z) = (2r+7) 71+11 %3|

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Q: 1. Differentiate G(x) = Ax+Bx+C 2. At what point on the curve y= 1 + 3e* – 3x is the tangent line…

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Q: Find the directional derivative of the following function at P(1, 0) in the direction that produces…

A: Given  fx,y = -3x2+4y3+2xe32y

Q: Let f(x) = 3x − ex + 5. (a) Find the equation of the tangent line to f(x) at x = 0.  (b) Find all…

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Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

Q: 9) Where is the function ht) = (t+ 5) differentiable?

A: Given         h(t)= t+51/3

Q: Find all values of x where the slope of the tangent line to f(x)=4x^2−3x+2 is 0. x = ___ If…

A: Topic = Derivative

Q: Find the derivative with respect to x of the function r4x t² F(x) = e dt.

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Q: The second derivative , for the function 7y+ 13z 3a2 is O y = 9

A: Given query is to find the second derivative of the function.

Q: 4. Write the equation of the line tangent to f(x) = (e* +2x +1)In(e* +2x+1), when x = 0.

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Q: Evaluate the derivative of the function r(t)=⟨lnt,3t+1,t2⟩ at t=1.

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Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Solve

Q: Find the derivative of the function. z = (4 – t)(1 + t?) `

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Q: Use the "First Principles/Limit" to find the derivative of the function S(t) = t2 – t, at t = -1/2

A: Given  S(t)=t2-t To find the derivative using first principle at t=1/2

Q: FIND THE SECOND DERIVATIVE OF THE FOLLOWING IN ITS SIMPLIFIED FORM. x = t/t-1 , y = t2/t2-1

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Q: Use differentials and the graph of f to approximate (a) f (1.9) and (b) f (2.04). To print an…

A: To calculate the approximate value of a) f(1.9) and b) f(2.04)

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: Q2: - Find the second derivative of the following function at x = 2 15 marks 1) y=+ V 2) y 3 (x +)…

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Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

A: Solution

Q: (d) Suppose that y(x) is a function and that y(2) = 1. Let y² + y = x. Using implicit differentian…

A: y2+y=x  Differentiating both sides with respect to x  ddxy2+y=ddxx    2y+1y'=1    y'=12y+1

Q: I. Find the derivative of the following. Show that the applicable differentiat rules has been used.…

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Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y-x) = 9 at x = 1. dy x-x B)…

A: Equation of tangent line is - y- y1 = m(x-x1)

Q: In what directions is the derivative of f(x,y) = xy + y at P(4,5) equal to zero?

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Q: Fin the second derivative of the fo!lowing functio 1. y = (x²+x+1)? 2. y = x (2x+1)' 3. y = V2a

A: (1) Consider the provided function, y=x2+x+12 Find the second derivative of the above function. Now,…

Q: Find the actual error when the first derivative of f (x) = In x at x = 2 is approximated by the…

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Q: Calculate the second derivative of the function y = f (x) defined by the equation x³ + y +3xy + 3y²…

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

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Q: Find the derivative of the following using the three-step rule Зх-1 1. у3D 2x+5 2. y=Va² +x²

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Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: Find the derivative of the following function: 2x-1 11. y = %3D Sx +2 13. y = V2x + 6 %3D

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Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: Let F(x) = dt. Find an equation of the tangent line to the curve y = F(x) at the point with…

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Q: In what direction is the derivative of f(x,y) = xy + y at P (3, 2) equal to zero?

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Q: Find the derivative of y = f(r) = VI(3r + ²). x(3x+x %3D

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Q: Given that f(x) = (x-2)/(x+3), find the slope of the tangent line at x = 2. %3D O a. 1/2 O b. -1/5 O…

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Q: Consider the function f(z) = V1+z -1 and find its derivative:

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Q: nd the derivative of the functionf(x) = v 5x+6 using the limiting proces A) S'x)= - 2 5x+6 Sx) = 2…

A: We are asked to find the derivatives of the function using limiting process.

Q: 9. Find the equation for the tangent line to f(x) = at A)9x+25 y=-34 B)9x+25 y =-24 r=-1 C)-9x+25y =…

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: Find dy for the given values of x and Ax. 3 y =x° - 6x +8; x = 1; Ax = - 0.1 - 6x + 8; x = 1; Ax = -…

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Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

Q: (d) Suppose that y(x) is a function and that y(2) = 1. Let y² + y = x. Using implicit differentian…

A: The objective is to find y'(2)and find the equation of tangent line to y(x) at x=2.

Q: In what directions is the derivative of f(x,y) = xy + y at P(8,5) equal to zero?

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Q: Find the derivative of the function at P, in the direction of A. 2 f(x.y) = 4xy- 4y, Po(6,8), A= –…

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Q: Show that, for a function f(x) with anti-derivative F(x), d s)ds f(x). %3D dx a

A: Suppose f(x) has an anti-derivate F(x), v(x) and u(x) are differentiable, then Leibniz's rule of…

Q: Q1) Find the tangent y = vx² – x + 7 at x = 2.

A: The detailed solution is as follows below:

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 7x + 8y.…

A: Directional derivative: - The partial derivatives of f give the slopes ∂f∂x in the positive…

Q: Calculate the second derivative of the function y = f (x) defined by the equation x³+ y³ +3xy+ 3y² +…

A: Explanation:

Q: Q2: A) Find an equation of the line tangent to the function of x² + (y-x)2 9 at x 1. dy x-x3 B)…

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Q: Find the third derivative of f (z) = T2x +I. fll! (z) =

A: Explanation of the answer is as follows