Use differential approximations in the following problem. A company will sell N units of a product after spending $x thousand in advertising, as given by N= 70x-x, 5sxs35. Approximately what increase in sales will result by increasing the advertising budget from $5,000 to $6,000? From $10,000 to $11,000? Find the differential dN. dN = ( ) dx The increase in sales from increasing the advertising budget from $5,000 to $6,000 is approximately (Type a whole number.) units. The increase in sales from increasing the advertising budget from $10,000 to $11,000 is approximately (Type a whole number.) units.

Q: Find the differential of the function y = (√1 + x)/(x − 1) and use it to estimate: The value of y…

A: Given query is to find the differential of y.

Q: Find the derivative of the function ?

A:

Q: An object of mass m is dropped from a helicopter. Assuming that air resistance is proportional to…

A: The velocity-time differential equation is: dvdt+kmv=g Since it is in the standard form of first…

Q: use implicit differentiation to find dy/dx and thend2y/dx2. Write the solutions in terms of x and y…

A: Here given

Q: Use differential approximations in the following problem. A company will sell N units of a product…

A: Given N=70x-x² where N is number of units and x is the spent in thousand dollars To answer the…

Q: Water is leaking from a pipe and the volume,V litres is decresing at the rate (6-t) litres per per…

A: Express the rate of decrease of volume V with respect to time t, as follows: The negative sign…

Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: The volume of a right circular cylinder is,

Q: Based on data from a research group, a model for the total stopping distance of a moving car in…

A: s=1.9v+0.064v2dsdv=1.9(1)+0.064(2v)dsdv=1.9+0.128v

Q: d²y nd by implicit differentiation if 3x² – 7y? = 14. dx?

A:

Q: Write a differential formula that estimates the change in the surface area S= 6x of a cube when the…

A: Given that surface area of cube s=6x2and side length change from x0 to x0+dxsolution:x=x0  and…

Q: The relationship between a certain real estate company's quarterly profits, P(x), and the amount of…

A:

Q: ydx 2. The exact differential what is the dxe")=

A:

Q: What is the value of the differential if f(x) = x + 2x - ! x = 8.4 and dx = 0.86. Round your answer…

A:

Q: Use differentials to approximate V42. b Express your answer as a ±- where a is the nearest integer.…

A: Use differential to find the (42)1/3

Q: Find the value differential equ of the arbitrary and the value c y'+4

A:

Q: Write the differential formula that estimates the given change in volume or surface. Then, use the…

A:

Q: Find the differential of the function. y = sqrt(2-t^6)

A: Find the differential of the function. y = sqrt(2-t^6)

Q: Use differentials to find the approximate value of y: (2x – 1)* when x = 0.98. O (E) None of the…

A: Given :f(x)=2x-14x=0.98

Q: dy Part II: Find the derivative ) implicitly. Show all work. dx 11. e" – 4x³ + 5y? = 10

A:

Q: Use differentials to approximate the change in cost corresponding to an increase in sales (or…

A: topic - application of derivatives

Q: Write a differential formula that estimates the given change in volume or surface area. Then use the…

A: S=4πr2 Differentiating with respect to r, we get ⇒dSdr=4π2r⇒dS=8πr dr Now when radius changes from…

Q: Given a function ƒ that is differentiable on its domain, write andexplain the relationship between…

A: The differentiable function is f on the interval I which contains a point a. The linear…

Q: Find the indicated derivative. dy for y = dx 1 – 2x2 x4 – 2x² + 4 %3D

A:

Q: The rate of change of the temperature of an object is given by T (t)=t·eª -0.1t min (a) Use the…

A:

Q: (a) Find the derivative. = In(x) – In(x - 8) dy dx (b) Find the derivative. y = In X - 8 dy dx %3D

A:

Q: 3.3 Find the derivative. y = 3x°e* %3D y' = II

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: f (x y) = x" + 6ly -10 what cre the first derivatives of the funchion?

A:

Q: Find the differential of the function. .6 y = V 3 – t

A: giveny=3-t6

Q: The equation for the amount Q of an antibiotic in the bloodstream at time t is Q = Ae-kt. %3D dQ 1.…

A: Q=Ae-kt Q is the amount of antibiotic in the bloodstream at time t Now we take derivative at time t…

Q: Find the derivative of the function y = 1ln(cos 2x)+4tan? (3x) Write the value of y (0) in the box…

A:

Q: Find the equation of a curve if d²y 4 = dx² (2x - 1)² the curve passes through (5, 2 ln3), and the…

A:

Q: Find the value of the derivative. dy if y =7- 4x2 dx |x= - 2 dy (Simplify your answer.) %3D dx |x= -…

A:

Q: 5

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 5xy + 2y. Po(-7,1), A=…

A: Given query is to find indicated derivative.

Q: Solve the problems below: 1. Find the 25 derivative of y=x. 2. Find the nth order derivative of the…

A: 1. Consider the given function, y=x20 the first derivative of the function will be,…

Q: Apply derivative of a differentiable matrix function?

A:

Q: Consider the following revenue function, where R is measured in dollars. R = 49x - 1.5x2 dR Find the…

A:

Q: dx 1 tent per day, dt the rate at which the total average number of COVID cases is increasing at x =…

A: Given,           The rate at which the total average of COVID cases is increasing at x = 10 tents…

Q: Find the differential of the function. = e dy =

A: y= e^(2x) dy = 2 e^(2x) dx

Q: v(t) = Vt* – Vt, en find the second derivative, "(t) = ...

A: We will use the following formula to find the second derivative i.e d/dx(xn)=nxn-1

Q: xdy – ydx The exact differential what is the d

A:

Q: use implicit differentiation to find dy/dx and thend2y/dx2. Write the solutions in terms of x and y…

A: Differentiating with respect to x, we get

Q: ind the second derivative in its simplified form 5. x= 1/t-1 , y= t/t^2 -1

A: Given :  x=1t−1  and  y=tt2−1

Q: r. Using differentials, approximate the percent error in computing the length of the hypotenuse.

A:

Q: What is the value of the differential if f(x) = x + 2x - x = 2 and dx = 0.63. Round your answer to…

A:

Q: Jse implicit differentiation to solve for dx a. x? - y? = 1 b. ху—х +2у В

A: Implicit differentiation: using implicit differentiation you can find the derivative of the function…

Q: 3x2 dx Jcos(x) # L sin(t) dt. Find the derivative of F(x) %3D

A:

Q: rcos(z) d (32) Find the derivative: dx V1- t?dt 1

A:

Q: dy Find the function y whose derivative - is 8.x+ 10 and y has a value of -2 when x is 1 dx y =

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.