The amount, A, of anesthetics that a certain hospital uses each week is a function of the number, S, of surgical operations performed each week. Also, S, in turn, is a function of the population, P, of the area served by the hospital, while P is a function of time, t. Write a type of chain rule that expresses the time rate of change of anesthetic usage, dA/dt, in terms of three of the derivatives described in part.

Q: Solve for the derivative of the function using chain rule. 4. f(x)= (x3+4)5/ 3x4-2

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Q: Find the derivative of the function. A) f(x) = In(x*Vx² - 3)

A: This problem can be solved by using the Chain rule as explained in step 2.

Q: Find the function whose derivative is 1-e2x

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Q: Write the function as a composite f (g(x )) and compute the derivative using the Chain Rule.…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Compute the derivative of f(x) (æ5 + 1)10

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Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: y=57x3+1-3

Q: Find the derivatives of the functions in Exercise

A: Given: y=1+x2x34-x-3 To Find: The derivative of the given function

Q: Find the derivative of the function. 21/4 1/2 +1

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Q: Use the Chain Rule to express the second derivative off o gin terms of the first and second…

A: Let y=f o g then we have to find the second derivative of y.

Q: Find the derivatives of the functions in Exercise

A: Given function is w=1z1.4+πz. To find the derivative of the functions.Solution: Power rule of…

Q: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

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Q: A Find the derivative using the three-step rule. 1. y = 11-9x

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Q: Determine whether each of the following statements is true or false, and explain why: The chain rule…

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Q: Find the derivative of the function g(x) et 5x - g'(x) =

A: We have to use quotient rule for derivative and use  d/dx(ex)=ex d/fx(ax+b)=a

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: Find the derivatives of the functions in Exercise

A: The given function is u=5x+12x.

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

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Q: Find the derivatives of the functions in Exercise

A: Given: y=x2+1x+5+1x Differentiating y with respect to x, dydx=ddxx2+1x+5+1x+ddxx+5+1xx2+1…

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

Q: Find the derivatives of the functions in Exercise

A: Find the derivatives of the functions in Exercise

Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Use the chain rule to find the derivative of lor67, 8x

A: To find the derivative of 106x7+8x6 using the chain rule. Solution: Chain rule of derivative states…

Q: Find a function whose square plus the square of its derivative is 1.

A: To Find a function whose square plus the square of its derivative is 1.

Q: Find the derivative of the function.

A: Given function is Differentiating both sides with respect to x, by using product rule of…

Q: Determine whether the following statement is true or false, and explain why. The chain rule is used…

A: Given: The chain rule is used to take the derivative of a product of functions.

Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

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Q: Find the derivative of all orders of the function. y3D x'-x + 5x-9 y3= %3D

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Q: Use the Chain Rule to express the second derivative of f ◦ g in terms of the first and second…

A: First, find the first derivative of the function, consider that the function f(x) and g(x) are…

Q: 1 3. f(x) = (-x4-3)2

A: Solve for the derivative

Q: Use the Chain Rule to find the derivative of the function. y (4x2 - 7)3 %3D

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Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

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Q: 5. f(x) = [(x + 5)5 – 1]4

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Q: f(x) = Vx2 + 5x-

A: We have given the function;

Q: Find the derivative of g(x) = J2x u²+1

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Q: Compute the derivative of f(x) = arcsin(x² e3=).

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Q: Use the chain rule to find the derivative of f(x) = 4( – 5æ" + 3z")" %3D

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Q: 2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second…

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Q: a derivative computation using the FTC and the chain rule t): df 13

A: Given : ddxFx3 =ddx∫13x3e-t2dt

Q: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

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Q: * Use the chain rule to find the derivative of

A: Given,        w = xy Here,         x=tan(t),   y=csc(t)

Q: Find the derivative of the given functions using chain rule. 1. f(x) = (2x + 1) 2. f(x) = (x² + 4x –…

A: To solve the following derivatives using chain rule and product as well as quotient rule.

Q: Find the derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: Compute the derivative of f (x) : = arcsin(x² e³«).

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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: In x g(x) = 2

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