Your weekly marginal profit (in dollars) from selling X newspapers per week is given by P'( x = 4 Compute the marginal profit when X = 50 and - interpret your answer in a sentence.

Q: Find the derivative of the function. f (x) = cube root of ( 1+ tant )

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

A: Given       f(x)=2sin x

Q: Find the derivative. 2 - - dy dx - if y(x) = 1 x + 3 dy dx ||

A: This question is based on Chain rule diffrentiation. d/dx{f(x).g(x)} = g(x)d/dx{f(x)} +…

Q: ) y = In³ )) (tanh²(scc '(x²)

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Q: Use forward, backward and central difference to estimate the first derivative of f (x) = In at x =…

A: Given function is fx=lnx and x=3 Step size h=0.01 We have to estimate the first derivative of fx=lnx…

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: What is the derivative of f (x) = cosh(x) + sinh(x)?

A: Given that f(x)=cosh(x)+sinh(x) find the derivative of f(x)

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 80x + 0.9x2 −…

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Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: Find the derivative of the function y = x tanh−1(2x)

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Q: The total derivative of f(x,y) = ylnx  is

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Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

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Q: An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

A: We will estimate the volume of cylindrical metal as following. Inside radius = 2 cm Inside height =…

Q: Find the derivative of the function. y = ek tan(V 5x) y'(x)

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Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

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

A: According to the question, we have to find the derivative of the function fx=arctan ex. The…

Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 70x + 0.7x² –…

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Q: Calculate the derivative.

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Q: Determine the gradient of the straight line which is tangent to the graph of f(x)= tan^-1(ln x) at…

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Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) %3D f (x) =

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Q: Suppose y = f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

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Q: The derivative of y= elanx + tan(e*)+ (tanx)® equals

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Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

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

Q: A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact…

A: given: A piece of wire, 370 cm long, is bent into an isosceles triangle. we have to determine what…

Q: 7) Find the average rate of change of the function A(x) = sin ( 2x - -) from x = to x =

A: A(x) = sin(2x - π/6) A(x2) = A(5π/6)          = sin(2*5π/6  - π/6)          = sin (9π/6)          =…

Q: Find the average rate of change of LaTeX: f\left(x\right)\:=3x^2+1 f ( x ) = 3 x 2 + 1 between…

A: Formula for average rate of change is f(b)-f(a)b-a.

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.5x² –…

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: Find the 2nd derivative of the given function fCt) = t² Int

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Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

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

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Q: Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 18x2 (x, y) = (…

A: As we know that the slope of the tangent on a graph represents by f '(x) and it is parallel to the…

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: Find the derivative. y(x) = x tanh−1(x) + ln (sqrt (1-x^2))

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Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: Find the values of x in the interval [0,2π] where the tangent line to the graph of y= sinxcosx is…

A: Given:y=sinxcosx,     [0,2π]

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: Find the derivative. f(x) = tanh(2 + e4x) f '(x)

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Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

Q: A bicyclist is riding on a path modeled by the function  f(x) = 0.04(10x − x2),  where x and f(x)…

A: given: A bicyclist is riding on a path modeled by the function fx=0.0410x-x2 where x and f(x) are…

Q: 1 f(x) = (x² + 3x)² at [2,3]

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Q: Find the derivative of s(*) - L Int dt 1+t

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Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

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Q: Determine the sign of the second derivative function as x varies. Where is f' positive? Where is…

A: Let's draw the graph of f''(x).