14. For the function f(x)=ax+bx²-5x+9, determine the values of a and b so that 5(-1)=12 and f'(-1)=3 .

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: = x2 - 4x + 1 with domain [0, 3] f has ---Select--- v at (x, y) = f has ---Select--- v at (x, y) = f…

A:

Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: Find an equation of the line tangent to f(x) =3 at x 3. %3D OA. y=xln 3+ (1– 3ln 3) OB. y=27(xln 3 +…

A:

Q: The derivative of the function y= (z+7x)5 is O 5(2 + 72) (3z?+7) O 5(7 +7x) (3x² + 7) O 5(r +7x)*(3²…

A: Topic- derivative

Q: 12. Given the function y=6x-2, find the derivatives O -6 O 2 O -2 Required

A: Topic:- calculus

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: 1. Find the derivative using chain rule. (a) f(x) = (x5 – 2)20 %3D Answer: (b) f(x) = V3r² + 1 %3D…

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

Q: 4) Calculate the first derivative of the following functions: 1. f(x) = In 2x2+1° 2. f(x) =…

A:

Q: Which among the choices has the first derivative that is e (2x+1) (x +3) ? Of(띠) 3D + 글z2 + 2x-8 O…

A: given function has first derivative is f'x=2x+1x+3    f'x    =2x2+7x+3

Q: 5. Find the derivative of the function. f(x) = x°/1- 8x x(16-136x) 2/1-Sr x'(16+136x) f (x)3D 2/1-8x…

A: The function is given by,

Q: Find the derivative of the following using First Principle. 4) y = -2x2 + 3x – 12 5) f(x) = x2 + 15x…

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Q: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

A:

Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: 5. If f(x)= 5x² + 2x+1 is an invertible function, find the slope of the tangent line to f^(x) at the…

A:

Q: 2. Calculate the derivative of the following. y = (x*- 3x2+5x) 3 y = tan (x2 + 5x - 2) А. B. (4x +…

A: Given  A. y=(x4-3x2+5x)3 B. y=tan2(x2+5x-2)C. y=(4x+3)3(x-2)2D. y=x2ex2-1

Q: Find the derivative of the function f(x) = 4v3x² – x. 12х - 2 A. V3x2-1 6х - 2 бх — 1 C. V3x2 –1 E.…

A: To find the derivative of f(x)=43x2-x

Q: if f'f′ is the derivativeof ff with 2∫1f'(x)dx=10∫12f′(x)dx=10 and f(2)=4,f(2)=4, then f(1)

A:

Q: Solve for the 2"nd derivative of the function f (x) = 3x5 – 4x3 + 7x² – 10. a. 15x* – 12x2 + 14x b.…

A: Given: fx=3x5-4x3+7x2-10 To Find: 2nd derivative of the given function

Q: If the utility depends only on the consumption of x and u (x) = ( 2a¯i + 3) (-4xi +2), is Marginal…

A: Given u(x) = 2x-12 + 3-4x14 + 2

Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

A:

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: 20. Find the derivative of the function. y = 9cos(2x) a. y'=-18sin(2x) b. y' =18sin(2x) c.…

A: Option (a) is the correct option. Differentiate y using the chain rule.…

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 derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A:

Q: Find the derivative of the function. (3x +5) f(x) = In (7x + 5)*(2x+ 8) 14 2 O a. 3x +5 + 7x +5 2x…

A: We have to check

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

A:

Q: The derivative of f(x) = 9z3 12 8. is %3D 3z f'(x) O f(r) – 9x?+ 12x 4 – 9r– 12x + 8e 7 O f(r) - 9x…

A:

Q: 3 Suppose 8 (x): 2(1- 5x)3 .What is the correct result of the derivative of g with respect to x? 45…

A:

Q: 2. Find y' by implicit differentiation. (1) xy-3x+2x =8 (2) 9x² +4y² = 25 (3) x²+2xy- y² =5 2 3 = 6…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

A:

Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

A:

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

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

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Q: In(4x Given f(x) = the derivative f'(x) is 4 1 4x 1 4x O 4 O z4z

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Q: In(4z+10) Find the derivative of the function f(z) = z'sin(9z + 12) + %3|

A: Given:- f(x)=x4sin(9x+12)+ln4x+10x3 To find:- Derivative of given function

Q: Suppose h(x) =23r +1 What is the correct result of the derivative of h with respect A h'(x) =3-23x +…

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: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

A:

Q: The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor…

A: A. Profit Function : P(X) = R(x) - C(x) P(x) = -0.04x2 + 800x - 130x + 40000 P(x) = -0.04x2 + 670x +…

Q: Compute the derivative of the function f(x) = S7+3x²' at the point 4, using the definition. Ex. 2.…

A: Derivative.

Q: What is the derivative of y = (2x)" O (2x)^(x) (1-In2x) (2x)^(x) (1+2 In2x) (2x)^(x) (1+In2x) O…

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

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Q: 2-х Find the derivative of y = Зx+1 -7 бх-5 6- А. (3х+1)2 В. (3x+1)2 7-6х С. (3x+1)2 D. (3x+1)2 Е.…

A: Proceed as shown below

Q: 1. Find the first derivative of the following. а. у%33x y = 3x² + 6 y = 2-1

A: