Exercise3. Determine the first and second derivative given the following functions. 1. f(x)=x - 9x² + 27x- 27 Answer: 3x –18x+27, 6x–18 1 2. y -1 Answer: 2 3. f(x)= 4(x° -1} Answer: 16x –16x , 48x? -16 1 4. y=(² -3x) Answer: 3x –12x +9, 6x –12

Q: 20. The fourth derivative of y = Jx -1 is 8 D.-은(x-1) 2 16 15 A. -(x – 1) В.- С.- 8. (X - 16 M| 00

A: This question is related to differentiation, we will use basic differention rules and results to…

Q: The function y(x) satisfies the equation 25x2-10y+1/2y2=25. What is the value of the second…

A: 25x2-10y+12y2=25 Differentiating with respect to x, we get…

Q: This is the complete problem. Calculate the derivative in respect to y of xy+2x^2 y−6y^3 x+y when…

A:

Q: Determine the derivative of y (x) = ( 3 x² + 11 x + 4 )³ e-6 x with respect to x. y '(x) =

A: topic - derivative of a function

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: 5x Find the equation of the tangent line of the function eb-y at the point (2, 10). (y – 5) = 5(x –…

A: WE HAVE TO FIND THE EQUATION OF THE TANGENT LINE OF GIVEN FUNCTION AT (2,10)

Q: II. Obtain the required order or level of derivative. 1. y = 3x5 + 4x³ – 4x + 1, find y" 2. f(x)…

A: Solve differentiate

Q: Find the derivative of the function. 10) y = (x + 1)2(x2 + 1)-3 2(x + 1)(2x2 + 3x - 1) (x2 + 1)4…

A: Given:        y= x+12x2+1-3

Q: Find the derivative of y with respect to x. + 1 5) y = sec-16x + -54 A) – 1 + (6x + 1)2 54 C) (6x +…

A:

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

A:

Q: 8. Compute the derivative of the following equation. (1) y = (x +1)3(2x – 2)2 (ii) y2-4x² y+x=16

A:

Q: 3x The equation of the line tangent to f(x) 1 at x = – 2 is x + 3 y = 10x +

A:

Q: Q1. Find the derivatives of the following: 1. y = -x 2. s = 5t - 31s + 3 4x 3. у 3 4. w = 3z2 - 5. у…

A: Please find the detailed solution in below images

Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x³ + y3 +3xy +…

A:

Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x'+y° +3xy +…

A:

Q: V3x – y + 6x*y? = 9y - 4.

A:

Q: Find the derivatives for each function. 1) y=e^(2x+x^(2))  2) y=2xe^(x^(2)) 3) y=ln((x+1)(2x+1))…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: Find the derivative of the following: y = 2x* + + 3a? – 7 O y' = 8x³ + a² + 6x O y' = 8x + 2æ² + 6x…

A:

Q: A) Find the domain and range (for TWO only) 1) y = V9 - V9x 2) y = V4 – x² 3) y= у 3 B/ Draw the…

A: given is 1) y=9-9x    y=9-3xdomain =x∈R : 0≤x≤9range ={y∈R : 0≤y≤3}

Q: Find the first and second derivatives of the functions w = 3z2e2z

A: Given:Assuming the given function is:

Q: 3. find the second order derivative 어: Xt xy t y= 16 2 4.

A:

Q: What is the derivative of y = (x2 + 1) e-3 ? O y = (x² +1) (e-3) + xe² - 3 O y = (x² +1) (e*-3) +…

A: It is required to find the derivative of the given function.

Q: B. Find the indicated derivative. -4 1. у: 2. x2 – 4y2 = 5; y" iy(3)

A:

Q: Consider the equation x² + y² + 4xy – 2y = 1. Then y can be viewed as an implicitly defined function…

A:

Q: Which among the choices has the first derivative that is equivalent to (2x + 1)(x + 2) ? Of (2)…

A: Solution:-  Step:1    Given:  f'x=2x+1 x+2

Q: 6e + 4 Find the derivative of g(x) 10r5 + 5x3 %3D = (z),6

A:

Q: Find the derivative of the function y = - 9 + 7x . dy II

A:

Q: r*y" + 31?y" =1+r

A: Consider the provided D.E,

Q: Find the derivative y′(x) of the function that describes the general equation of a second order…

A:

Q: Find the derivative of the given function y = (2x+ 5)v4x – 1

A:

Q: Find the indicated derivative. dt for y(2.4t-3t)(2t+1.1)

A:

Q: Find the derivatives of the functions y = (2x + 1)√2x + 1

A: we have to find the derivative of y=(2x+1)2x+1

Q: 1. Find the derivative of the function y = (x² – 1) (2x² – 3). | 2. Differentiate g (x) = x+1l x+2 °…

A:

Q: Find the derivatives of the functions y = (1 - t) (1 + t2)-1

A:

Q: Solve the following problems: Use Implicit Differentiation of functions of several variables to find…

A:

Q: Find the first and second derivatives of the function.

A:

Q: 1. Find the derivatives y = x' /4x -1 y =- y= (2x + In x)? V1-2x 2. If f(2) = 4, f'(4) = 6, f'(2) =…

A: We will use the formula (uv)' = uv'+u'vuv' = vu'-uv'v2(f(x)2)' = 2f(x)f'(x) 1) Consider y = x24x-1y'…

Q: Q3. Find the derivatives of the functions 2x + 5 a) y b) w = (2x – 7)(x + 5) Зх — 2 5x + 1 с) и 2 Vx

A: We have to find the derivative of the following functions a)  y=2x+53x-2 b) w=(2x-7)-1(x+5) c)…

Q: 4. What is the SECOND derivative of the given function? * y = 3x³ - 2x² + x - √ y" =9x² - 4x + 1 y"…

A:

Q: B. Find the indicated higher order derivatives *** (1+x)² 2. y"'if y = x2

A:

Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

A:

Q: Q1)If f=x+y find second derivatives of fcx, fxy?

A:

Q: 9. The derivative of the graph x+y² D5 with respect to time is c-2y+ 20 C. a. y +x d. -y 2x +2y

A: Q 9 Given that: The graph: x2+y2=25

Q: B) Find the derivatives of the following functions 2) y=2 Vx-1 sec Vĩ 2 (x+1)10 (2x+1)5 7) y=ttanh…

A:

Q: Find derivatives of the functions defined as follows: y = -4e-0.3x

A: Our Aim is to find the derivative of the function given below:-y=-4e-0.3x -(i)

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)…

A:

Q: 18. Up to what derivative is the derivative of y = x6 + 2x5 - 4x4 + 7x³ becomes 0.? a. yv b. yu c.…

A: