43. City urbanization City planners model the size of their city using 1 t<50, where A t2t20, for 0 50 the function A(t) is measured in square miles and t is the number of years after 2010. a. Compute A'(t). What units are associated with this derivative and what does the derivative measure? b. How fast will the city be growing when it reaches a size of 38 mi2? c. Suppose the population density of the city remains constant from year to year at 1000 people/mi2. Determine the growth rate of the population in 2030.

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: how do you indicate the derivative with any method: g(t) = 3/t^5; estimate g'(1)

A: Write g(t) using negative exponents to get rid of the fraction. Then use exponent rule.…

Q: Suppose that your friend, who is concerned that you are 100 pounds overweight, has studiedthe diet…

A: The given function shows the weight Wt=300-15 lnt+1 Find the derivative of weight function:…

Q: 1. The velocity of a rocket is given by v(t)= 2000 ln 14x10 14x10 – 2100t -9.8t,0sts30 where v is…

A: Given vt=2000ln14×10414×104-2100t-9.8t , 0≤t≤30 and t=16, ∆t=2 and True value = 29.674

Q: 1. If y = x³ + x - 5 then what is the derivative of y with respect to x?

A: Derivative of a function

Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

A:

Q: 8 Find the derivative of the function: 1) g(x) = V1+ t² dt 2) g(x) = d 3x 1 1+4 3) g(y) = , tsin2tdt

A: Apply lebneitz integral rule

Q: Determine the first derivative of the ff. function y = ln| le* – 1/

A: We have to find the first derivative of the function: y=lnexex-1 We know the property of logarithm,…

Q: 6. Determine the derivative of the following functions. Do not simplify. (a) y = 2t° +t+ e² 2 (b) y…

A: Given:           (a) y=2t5+t+e2Differentiating with respect to…

Q: Can you help me with this problem step by step?

A: Given:

Q: Find the derivative of the function y = coth−1 (e2x)

A:

Q: Find the derivative of y. 30) y- In (sinh 9x) 1. B) sinh 9x A) coth 9x C) 9 csch 9x D) 9 coth 9x

A: Derivative

Q: 4 Find the derivative of the function y= f(x)= Jx(x-8). %3D

A:

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: Find the derivative of the function. 7x 7x flu) du J3x 0 fu) 3x d du g(x) Hint: fu) 3x u5 g'(x)

A: To determine the derivative of the function.

Q: Зх + 7 Calculate the derivative of f(x) at x = 0. Give an exact answer in decimal form. 4х — 5 f'(0)…

A: *The given function f(x) is, f(x)=3x+74x-5 Apply quotient rule on the above function to get the…

Q: 2. Find the derivative of (x + 1) /x. 3. Given the equation: y = (eln )?, find y'.

A:

Q: find the derivative of y with respect to the given independent variable  1. y = 3-x    2. y = 2(s2)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: a.) z= 5.

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

Q: 3 (a) Find the derivative of the function y = (t3 + 1)10 dt

A:

Q: can you please reply quickly For the flow-dependent function of hydrological energy power x=6, find…

A:

Q: at x: つ:8ー5x, atx=e

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

Q: Suppose the derivative of H(s) is given by H'(s) = s²(s² + 6)(s + 4). Find the value of s in the…

A:

Q: A. Find the derivative of the given function at a given number 1. y =3x -2 at f(1)

A:

Q: Suppose the derivative of H(s) is given by H'(s) = s²(s² + 6)(s + 4). Find the value of s in the…

A: Given derivative function - H'(s) = s2s2+6s+4Let's find the critical point of the given equation -…

Q: 1) Find the derivative of y with reference to < Y 블+름 2y Y

A: Here is the solution:

Q: et y = (xº + 4)*. + 4)*. se the General Power Rule to find the derivative.

A:

Q: 8) f(x)= T+x²

A:

Q: 1. Find the derivative of the following functions: (а) у %3D 3x5 — 5х3 — 8х + 8 (b) y = x-5 + x-8 –…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 5. a) Find the first order derivative of the following function. y x° In x

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: IV. Obtain the 2nd Derivative of the given function. 7. 4y – xy? 1

A:

Q: 9. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters)…

A: We need to find velocity.

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function

Q: Can i get help step by step?

A: Given,

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

A:

Q: 3. Find the derivative of y with respect to the appropriate variable. x y= 6sinh :

A: Solution: y=6sinhx3

Q: 4+ 9e Use the Quotient Rule to determine the derivative of the function w(s) 7e + 8

A:

Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

A:

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: c. Find second derivative implicitly for y + 2Re *y = 3R.

A:

Q: (2) Assume that we have a Cobb-Douglas production function for a certain industry: Q = CL°K®, where…

A:

Q: 4. The derivative of the function f(x) = r +3) is

A:

Q: Can you help me with this problem step by step?

A: Consider the given function:

Q: 3. Find the derivative of y = | (12 +1) dt.

A:

Q: 2. Determine the true error and the relative true error of the first derivative of f(x) = 2.5-* %3D…

A: Solution is below

Q: dy Y= x ²x-> メ =人

A:

Q: e) The function f(x) = log(x)log(x) with x %3D Jse fzero to find a zero of its derivative. What is…

A: The given function is f(x)=log(x)log(x); with x≥1

Q: y=x4Inx

A: Topic = Derivative