The number of bacteria after t hours in a controlled laboratoryexperiment is  n= f(t).(a) What is the meaning of the derivative f'(5) ? What areits units?(b) Suppose there is an unlimited amount of space andnutrients for the bacteria. Which do you think is larger f'(5) ,or f'(10) ? If the supply of nutrients is limited,would that affect your conclusion? Explain.

Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Find the derivative of the function y = ln(tanh x/2)

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Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x = 5 using a…

A: Given function is y=cosx. We have to find the first derivative of y=cosx at x=π2 using a value of…

Q: 3) Find the second derivative of y with reference to x. xcosy = y

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Q: part ii, thank you very much.

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Q: (a) Find the average rate of change of f(x) from x = 1 to x = 2. 7 (b) Using the definition of the…

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Q: . Find the equation of a line tangent to the graph of f (x) = cotx at x = T/4. .Find the derivative…

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Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 1 using a value…

A: The two-point forward difference formula to calculate f'(x) is f'(x)=f(x+h)-f(x)h, where h is the…

Q: 14) Find the first derivative of f(x)= 2*2*

A: The derivative of ax is axlna. The derivative of xn is nxn-1, where n is any integer. The chain rule…

Q: 10) Find the second derivative of k(z) = 4 cscz.

A: Given: kz=4cosecz for finding second derivative of given function, we find first derivative then…

Q: 5) Find the second derivative of f (x) = %3D ex plify your answer as much as possible

A: fx=1-2xexTo find the second derivative

Q: 1. f(x) =In (ta n"x)

A: Given query is to find the first derivative of the expression.

Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

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Q: 8. Find the derivative of the function. y= In(1+x)

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Q: Compute central difference approximations for the first derivative of the function, y = e'cos(x?),…

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Q: 7.) f (x)> (3x+2)(5x-2)

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Q: Find the derivative of the function y = ln(9 – e-"). f'(x) =

A: Given that y=ln(9-e-x) To find : Differentiation  y'=f'(x)=ddx(ln(9-e-x))=19-e-xddx(9-e-x)=e-x9-e-x

Q: Determine the first derivative of the ff. function y = Vxe2* cos x

A: Derivative of a function gives the tangent of the curve at a given point. Derivatives are used to…

Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

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Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.

A: Answer and explanation is given below..

Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x =; using a…

A: The three-point midpoint rule to calculate f'(x) is f'(x)≈f(x+h)-f(x-h)2h, where h is the step size.

Q: What is the derivative of: y ln x − x ln y = 1

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 5. First compute the derivative of f(x)= Vĩ and then use it to: a. Find the equation of the tangent…

A: Given equation of curve is fx=x. Power rule of differentiation states that: ddxxn=nxn-1…

Q: (d) y = xnz²

A:

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

A: See the details solution in below

Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: The size of a population of butterflies is given by the function. p(t)= 6000/(1+49(0.6)t) where t…

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Q: a.) z= 5.

A: We will find the second derivative of the given function in the following step.

Q: at x: つ:8ー5x, atx=e

A: Given:  F(x) = x3 - 5x ...(1)       and the…

Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

A:

Q: Apply central divided difference approximation (CDD) to find the first 5 derivative of F(x) = e0.8x…

A: To find the first five derivatives of fx=e0.8x when x=24 using central divided difference…

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…

A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: Compute backward difference approximations for the first derivative of the function, y = log(x² +…

A: We have to compute backward difference approximations for the first derivative of the function,…

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

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

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Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

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: 1) Find the second derivative of f (x) = 24 . %3D

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Q: The derivative of y=eSinh/x +cosh¬/x equals

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Q: 3. Find the derivative of: y = csch¬(In (sech(sec()))).

A: Note:Two questions submitted simultaneously, kindly upload question 2 separately.

Q: What is the first derivative of g(x) = ln #*+1? x2

A: Derivative of ln(x):       ddx(ln(x))=1x Division rule of derivative:-…

Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: 8. Find the derivative of the function (t)= 3sin(arccost)

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Q: 24. Find the first order derivative with respect to x of the function u = log(x+ x .

A: The solution for the above question is as shown below.

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

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Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

A: