Q. 2 (a) find the derivatives for the following functions. (i) y = 5x - 6x (ii) (x²+5) / (x+3) (iii) y = (4x-1) (x² +6x - 3) (iv) y = (3x? + 2x + 1)s

Q: 1. Find derivative of given function defined as follows. 7-29-22 y = (8x²-3x³) ³

A:

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: 5. Find the first and second derivatives of y if y is a function of r defined implicitly by x* + y*…

A:

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

A: Given,  y=−4e−0.3xFormula→ddxaex=aex  where a is constant.

Q: Q-1- Find the derivatives of the functionS 1- Y+In (xy) = |

A:

Q: 1. Find the derivative of each of the following functions using chain rule: y=3x* (x* -2) a)

A:

Q: Use the chain rule to calculate the first derivative of the following 19. (2x + 6)3 20. In (3x - 2)…

A:

Q: 1. Find the derivative of the following 9x²-4x+9 a)y = 2(x²-3)²√√3x-1

A: We know that the derivative of a function fx is the rate of change of that function with respect to…

Q: Find the second derivative of the function f(x) = 2 – 3x + 5æ/2 – 7e" . 15 f"(x) = –3+ 2 7e" f" (x)…

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: 1 Find the derivative of f(x) = v2 – 3xª 2 -4 |

A: We use chain rule to find derivative

Q: Evaluate the derivatives of the given function for the given value of x. y" = (4x^2-5x+4)…

A: For evaluating derivatives we put x =5 in the given equation.

Q: 1. Determine the first derivative of the functions below with the rules for deriving the function:…

A: A Given function is y=4x3+32. Use formula ddxxn=nxn−1 Differentiate  y=4x3+32 by using the chain…

Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

A:

Q: Find the second derivative of the function y=x(x² – 1) (А) 4x(5х2 - 3) в) 2x(5x2 - 6) (с) (2х -…

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: Find the first four derivatives of the following functions: 1. y = 4x³ + 12x² + 7x 2. y = 2x5 + 6x²…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the derivatives with respect to x of the function 2-3x2 A-2x2//2-3x2 -3x /2-3x2 9-2x²/ /2+3x² D…

A:

Q: What is the derivative of y = (4x2 + 9x + 1)e-2? O no correct answer Oye-2 [2(4x² + 9x + 1) + (8x…

A: Solve the following

Q: =) f(x) = x²e¬4x

A:

Q: 2 3 1. Determine the derivative to y² = x³ + y² + 2xy

A: Given problem:- Determine the derivative to y2 = x3 + y3 + 2xy

Q: Find the derivative of the following functions. 1. y= -7x^-5 + 4x^2 -19x + 2 2. y= 5x^3-15-25 3. y=…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 5. Find the derivative of y= x' +2x -1

A:

Q: 7. Find the first derivatives of each of the following: a. y= 10x³ – 4x² + 6x – 12 b. g(x) = x'e" c.…

A:

Q: 27. The first derivative of y = is (4x+1) -24 b. 24 C. -6 6. (4x + 1)+ (4x + 1)+ (4x + 1)4 (4x + 1)*…

A: y=-2(4x+1)3

Q: 5 What is the derivative of5a2 + 10x + ? A None of the given choices B 10x + 10 + 3x2 10a4 + 10a³ –…

A:

Q: 9. Find the derivative of y = xe3-x (A)e3-x? (B) 0 (C) e³-x*(1– 2x?) (D)–2xe³-x² (E) e3-x*(1+ 2x²)

A: Given : y = xe3-x2

Q: Find the derivative of the function. x3 y -1 -2x3+3x2 y's (x- 1)2 y'= 2x-3x2 (x-1)2 y'= 2x3+ 332 (x-…

A:

Q: 1. Find the second derivative of f(x) = x5 – 4x + 1. а. 5x3—4 ь. 20х3 с. -20х3— 4

A:

Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: 1. Find the first derivative of the following functions: y = f(x) = -(2x + x³)-2 + 4x (2x+4)² (a)…

A:

Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)3 5. h(x) x+5 = x2-9, 6. A(x) = v3x3 +…

A:

Q: Find the first derivative of the following: y=3x^2-x-2

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Find the derivative of the function. y = (3x + 1)°(x+ - 6)° A y=(32x +9)(3x +1) (x*-6)° B y' = 9(3x…

A:

Q: What is the value of y' at x=-4 is ______? Evaluate the derivatives of the given function for the…

A: The function is given by y = 5x2-x+53-3x-x2 To evaluate : The value of y' at x =-4

Q: 1. Find the derivative of the following f) y = (2x − 1) ( x³ − x) + √x[2(x³ − x) + (2x − 1)(3x² −…

A:

Q: Find the value of x for which the derivative is zero of Y =x +4x - 3x – 5

A:

Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)³ 3 5. h(x) x+5 = x2-9, 6. A(x) = v3x³…

A:

Q: Match the functions in Column A with their derivatives in Column B. 1. f(x) = 4 А. f'(x) = 8x 2.…

A:

Q: Find derivatives of the following functions: y = (4x + 3)/ln[2x2 + 3x - 5] y = 3( e2x + e-2x )(x2 -…

A:

Q: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

Q: Find the derivative of y = x²( - %3D x2+1

A:

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

A:

Q: y = (4x + 3)/ln[2x2 + 3x - 5] y = 3( e2x + e-2x )(x2 - 4

A:

Q: Find the derivative of the function y = In(x /x² + 14 X Vx²+14 1 Vx²+14 1 x²+14 x2+14

A: Topic:- derivatives  Note:- as per our guideline if more than one question uploaded than only first…

Q: Find the First and second derivative of the given y=-x2+3

A:

Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

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: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 A) - = 2(x+ 1)(x2 + 1)-4(2x2 - 3x - 1) B) Y =-2(x +…

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.