The sales of a product S(in thousands of dollars) are given by

S= 600x/x+40

where x is the advertising expenditure(in thousands of dollars)

(a) Find the rate of change of sales with respect to advertising expenditure.

(b) Use the second derivative to find how this rate is changing at x=20.

(c) Interpret your result in part (b).

### Want to see the full answer?

Check out a sample Q&A here*arrow_forward*Check out a sample Q&A here

*star_border*

## Related Calculus Q&A

Find answers to questions asked by students like you.

Q: How do you find the derivative of the product of two functions that are differentiable at a point?

A: We can find the derivative of the product of two functions using product rule of differentiation.…

Q: Find the derivative of the function f(x.y) = tan -1 y at the point (4, - 4) in the direction in…

A: Click to see the answer

Q: How do you find the derivative of the sum of two functionsƒ + g?

A: we have to determine how to determine the derivative of the sum of two functions that is f+g.

Q: How do you find the derivative of the product of two functionsthat are differentiable at a point?

A: Consider the two functions f(x) and g(x). f(x)·g(x)'=f'(x)g(x)+g'(x)f(x). Here f(x)·g(x)' represents…

Q: Find the 3rd derivative of the function y=excosx.

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get

Q: Find the 3rd derivative of the function y=excosx.

A: Click to see the answer

Q: Find the 3rd derivative of the function y=xsinx

A: Click to see the answer

Q: Find the 3rd derivative of the function y=xsinx.

A: Click to see the answer

Q: What is the derivative of ex? What does it mean that the derivative is equal to the value of the…

A: Explanation of the solution is given below...

*question_answer*

Q: Solve for the derivative of x² – y² = 9 using implicit differentiation %3D

A: Given : x2 - y2 = 9To find : y'

*question_answer*

Q: Calculate the second derivative of the function y = f (x) defined by the equation

A: We have to find the second derivative of given equation.

*question_answer*

Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

*question_answer*

Q: Find the derivative of the function f(x,y) = x +xy + y at the point (- 2,- 1) in the direction in…

A: Click to see the answer

*question_answer*

Q: Find the derivative of the function f(x y) = tan-1Y at the point (5, -5) in the direction in which…

A: Click to see the answer

*question_answer*

Q: Can you help me step by step?

A: To differentiate the given expression y=f(x)

*question_answer*

Q: How do you find the derivative of a constant multiplied by afunction?

A: Constant Multiple Rule. The derivative of a constant c multiplied by a function f is the same as the…

*question_answer*

Q: How do you find the derivative of a constant multiplied by afunction?

A: If f(x) is any function and let y=cf(x) function f(x) multiplyed with a constant, c is…

*question_answer*

Q: Find the derivative of the function. y = tan−1 (square root of x - 4)

A: Consider the given function. y=tan-1x-4 The objective of the problem is to find the derivative of…

*question_answer*

Q: Find the derivative of the function. 2 x* + 2 .2 y 2 y' =

A: y = x2+2x2-25we know:ddx xn = nx(n-1)ddx f(g(x)) = f'(g(x)) . g'(x)

*question_answer*

Q: Find the derivative of the function. y = etan(x)

A: Click to see the answer

*question_answer*

Q: Find the derivative of the function. f(x) = x ex

A: Click to see the answer

*question_answer*

Q: Match the graph of the function with the graph of its derivative.

A: Assume that y = 0 at x1 and x2 in the given graph. From the given graph, it can be concluded that…

*question_answer*

Q: Match the graph of the function with the graph of its derivative.

A: Click to see the answer

*question_answer*

Q: Find second derivative x⅓+y⅓=a⅓

A: Given, x13 +y13 =a13

*question_answer*

Q: Find the derivative of the function. Vs - 1 f(s) = Vs +5 l'(s)=]

A: Given query is to find the derivative of the function.

*question_answer*

Q: Find the derivative of the function. Vs - 4 f(s) = Vs +2 f'(s) =

A: Click to see the answer

*question_answer*

Q: 3. Find the derivative of y = csc" (sec x), 0<x< 2n.

A: Given ddx(arccsc(sec(x))Let sec(x)=uWe know that ddx(cosec-1…

*question_answer*

Q: .Find the derivative of the function: y =x² +8sin .

A: To find the derivative of y.

*question_answer*

Q: Find the derivative of the function. y- tan-(V-8

A: In this question, we need to calculate the derivative of the given function.

*question_answer*

Q: Find the derivative of the function f(x) = 2sin x %3D

A: Given f(x)=2sin x

*question_answer*

Q: Find the derivative of the function f(x) = 1+ ex

A: First I have written the formula of quotient rule of derivative, just use the rule for given…

*question_answer*

Q: Find the derivative of the function f(x.y) = tan -1y at the point (- 9,9) in the direction in which…

A: To find the derivative of a function at a point (-9, 9) in the direction in which the function…

*question_answer*

Q: Find the derivative of the function y = 2x − cosh √x

A: The given function is y=2x-cosh x. Obtain the derivative of y=2x-cosh x as follows.

*question_answer*

Q: Find the Derivative of the hyperbolic function (3.11): y=sech(x)*(1+ln(sech x))

A: Click to see the answer

*question_answer*

Q: 5. Find derivative y' 4=x²(nx %3D

A: Given: y=x2lnx Product rule: When y=u(x)v(x) dydx=dudxv+udvdx

*question_answer*

Q: Find the derivative of the function. h(x) = ex² - > x + 5 %3D

A: Click to see the answer

*question_answer*

Q: What is the derivative of (x^2+1)^x?

A: Use the lograthim to find the derivative of given expression.

*question_answer*

Q: How do you find the derivative of the quotient of two functions that are differentiable at a point

A: Let rx=fxgx be a function.

*question_answer*

Q: Find the derivative of y = csc-1√x

A: Given: y = csc-1 √x Let u = √x Then the function becomes y = csc-1 u.

*question_answer*

Q: Find the derivative of the function. y = 3 tan-(x - V1+x²) II

A: Consider the given function

*question_answer*

Q: Explain the relationship between the slope and the derivative of ƒ(x) at x = a.

A: Given function is fx at x=a

*question_answer*

Q: Find the equation of the line tangent to the graph of the function f(x)=x-2x^2 at x=1 use the…

A: The equation of the curve is: f(x)=x-2x2

*question_answer*

Q: State the notation/symbol for: derivative of y with respect to x derivative of f(x) second…

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

*question_answer*

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 x/2

A: We have to find derivative of y with respect to the appropriate variable: y=cosec-1x2 Rewriting the…

*question_answer*

Q: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…

A: Click to see the answer

*question_answer*

Q: Find the derivative of the function. y = arctan 1 + x 1 - X y' =

A: Click to see the answer

*question_answer*

Q: Define the second derivative of f. If f(t) is the position function of a particle, how can you…

A: Second derivative is derivative of the derivative. Therefore,…

*question_answer*

Q: What is the first-order derivative of y = x^y?

A: Click to see the answer

*question_answer*

Q: Determine the derivative of f(x)=ln(x√x^2+1).

A: Click to see the answer

*question_answer*

Q: Find the derivative of y with respect to x Y=5 ln (3 ln x)

A: Given, y=5 ln (3 ln x) We have to find derivative of y with respect to x.