We are told that the number of units of weekly output of a product is Q(x) = 200x + 5x² where x is the number of workers on the assembly line. Currently, there are 81 workers on the assembly line. We want to find Q'(x) and estimate the change in the weekly output caused by the addition of one worker. We start by finding the derivative, Q'(x). Q'(x) + 5. II

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

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Q: Find the derivative of function.

A: To find the derivative of the given function                                                y=log…

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

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Q: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: find nth derivative of y=x/(x+1)^4

A: To find the nth derivative of the function y=x(x+1)4=x+1-1(x+1)4=1(x+1)3-1(x+1)4

Q: 5. y= 2arctan(vx)

A: We need to evaluate the derivative of the following function y = 2arctanx

Q: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

Q: what would be the output if the 2nd derivative is negative

A: We know that for a function y = f(x), the points of extremum are obtained if the first derivative of…

Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: ; Compute the derivative of the function: f (x) = (+ Inx)² а.

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Q: When the graph of the derivative is positive then the graph of the antiderivative will be…

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Q: Find the derivative of the function y = x tanh−1(2x)

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Q: If the sign of the first derivative function is positive, the main function f(x) is decreasing.

A: We have to tell If the sign of the first derivative function is positive , the main function f(x) is…

Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

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Q: Find the derivative of the function. y= log sv7x +3 dy dx I3D

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Q: Find the derivative of y=sinh-17x

A: Given:y=sinh-17xHyperbolic Identity:cosh2x-sinh2x=1Differntiation formula:ddxsinx=cosx

Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

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

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Q: Find the first derivative of: y = sinh e2" O y e2 cosh e2# 2e2" cosh e2" O y' 2 cosh e2 O y = cosh…

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Q: Find the derivative of the function y = 2x arccos x − 2√(1 − x2 )

A: If the two functions f(x) and g(x) are differentiable (the derivative exist) then the product is…

Q: y = e* (In x)² %3D

A: Here we want to find the first derivative of the given function. For finding the derivative we use…

Q: 11) Find the first derivative of y = (lnx) 4

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Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: Compute the derivative: x4 – 4 d - at x = 2 dx x2 – 5 - The derivative is:

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Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: What is the first derivative of the expression (xy)× = e?

A: See the details solution in below

Q: Find the derivative of the function y = cosh−1(3x)

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Q: Find the derivative of the function y, below. y = 2x(ln x + ln 5) – 9x + v2 dy dz ||

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Q: Calculus 11th Edition - Ron Larson Please assist with the question below. Please show &…

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Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

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

Q: find the 2nd derivative of the function defined implicity by the equation x^1/3+y^1/3=80

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Q: Find the derivative of y with respect to x if y = (5x2 – 10x + 10) e - 6x y' =

A: We have to find the derivative of y with respect to x.

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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Q: find the derivative of y with respect to the givenindependent variable. y = log2 5θ

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Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: Find the derivative of 5e* 1. y = e 6x 3. y = 2x+3x 2. y = e* + e3x 4. y = (e* + ex)1/2

A: Quotient Rule of differentiation : ddxuv=v.dudx-dvdx.uv2 deaxdx=aeax dxndx=n.xn-1

Q: f y = (sin x)x b

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Q: Find the derivative of the function. 9 y =- Vx + 1

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Q: Find the second derivative of the equation below evaluated at y = 1:

A: Given that: The implicit equation 4 e y + x y = 4e.

Q: 10. Solve for the derivative of y IMPLICITLY 22 + vx³ + 2y= y²

A: Topic =Derivative

Q: If 4x2+3x+xy=20= and y(5)=−19, find y′(5) by implicit differentiation. Enter exact values.

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Q: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: Approximate the derivative of y=x² at x=1 by forming small changes

A: We have to find the derivative of the function y=x2 at x = 1 by forming the small changes.

Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

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Q: find the derivative of y with respect to the givenindependent variable. y = log3 (1 + θ ln 3)

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Q: Find the 1st derivative of the function: y = 4(Vx + 1)5

A: Given that: y=4(x+1)5