Suppose that the revenue from selling x washingmachines isr(x) = 20,000(1 - 1/x)dollars. Use the function r'(x) to estimate the increase in revenue that will result from increasing production from 100 machines a week to 101 machines a week.

Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: Find the function whose derivative is 1-e2x

A:

Q: Find the second derivative of the function f(x) = 3*(square root of x+2 divided by 2x +1

A:

Q: Find the derivative of f(x)=ln(x^3-x+2)

A:

Q: Find the derivative of f( x ) = 2° log3(z + 2.5) f'(x) =

A: The first derivative of the function is . The product rule of the differentiation is .

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=3f(x)+1x. If the…

A: Derivative of a function using the formula f′(x)=3f(x)+1x and f(3)=6. We know that approximate…

Q: Find the instantaneous rate of change in f(x)= 3/x^2 at x=-2.

A:

Q: find the derivative using logarithm of y= (x+2)^2

A: Take ln on both sides Then differentiate both sides with respect to x

Q: Find the function whose derivative is Inx+1.

A:

Q: what would be the output if the 2nd derivative is negative

A: We know that for a function y = f(x), the points of extremum are obtained if the first derivative of…

Q: State the derivative. Do not simplify. f(x) = log(x) + log₂ (x)

A:

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: Find the derivative of the inverse function to f(x)=ex-e-x

A:

Q: In(x²) What is the derivative of

A:

Q: Find the second derivative of the function f(x)= x^4 x sec(x)

A:

Q: Compute the derivative in terms of log for y=log(xe^(-3x))

A:

Q: x+1

A: By using the formula you can solve the given problem as follows :

Q: Solve for the second derivative of f(x)=2x-2/x+5

A:

Q: Find the derivative of f( x ) = log3(x + 6.5). f'(x) =

A:

Q: f (x) = ln(x · 5*)

A:

Q: Find the derivative of y =log2x

A:

Q: Evaluate the 3rd derivative of y= x5Tan(x4) if x=4

A:

Q: find derivative y=square root of (1+ x times e^-2x)

A:

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: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: The number of licensed drivers in a country (in millions) can be approximated by the function g(x) =…

A: Here, the given function is: g(x)=178.277x0.065 where x is the number of years and g(x) is the…

Q: Find the derivative of f(x) = log35x2+1

A:

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: Solve the derivative of f(x)=−1/√2 x +2x

A: Given- fx=-12x+2x To find- The derivative of the above function. Formula used- Using the power rule…

Q: Find the derivative of the function. y= log 4- x

A:

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

A:

Q: Find the 1600th derivative of f(x) = xe¯X. f(1600)(x)

A: The given function is fx=xe-x. Observe that,…

Q: Find the derivative of the function. f(x) = ln 2x/(x + 3)

A:

Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: Find the derivative of the function y = log3(x2 − 3x)

A: Consider the following: y=log3x2−3xDifferentiate w.r.t.…

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Find the derivative of the function. f(x) = ln(4x)   f '(x) =

A: Given function

Q: Find the thousandth derivative of f(x) = xe -x

A: Given function,  f(x) = xe-x  To find the thousandth derivative of f(x)

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

A: instantaneous rate of change of a function is differentiation of function at that point

Q: Calculate the derivative of the function y=log2 x ln (2x) at x=1.

A:

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

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

Q: What is the derivative of the function  x^8(ln(x))?

A: To find the derivative of the function x8(ln(x)) as follows.Redefine the function as follows.

Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: Find the derivative of the function. h(x) = log4(x + 9) h'(x) =

A: Topic = Derivative

Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

A:

Exponential Growth Model

The relation that represents an exponential function is: