Chapter 4, Problem 20RE

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Differentiate the function. 5/1-x y = y' =

Please provide me with the solution and work to the question. Please try to dumb it down so I can understand it.

et Consider the function f(x) = Compute the derivative of this function. 5 + et

Quantity vs. Rate-of-Change The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled by N(x), million senior citizens, where x is the number of years after 2000. N(x) = 0.03x2 + 0.315x + 34.23 (a) Find the derivative of N(x) and use it to complete the model statement below. (Refer back to Section 3.2 of your text (or ebook) for simple derivative rules.) N'(x)= --select units-- O gives the projected rate at which the number of senior citizens is changing x years after 2000, for the years 1995 through 2030. Use the appropriate function from above to answer questions b through d. (b) What is the projected number of senior citizens in the year 2025? (Round your answers to 3 decimal places.) million senior citizens (c) What is the projected rate of change of the number of senior citizens in 2025? (Round your answers to 3 decimal places.) million senior citizens per year (d) The Census Bureau predicts that in 2030, 20.1% of the U.S. population will…

Using the chain rule, derive the formula for the derivative of the inverse sine function.

In Exercises 93-98, let f(x) = sin x, g(x) = cos x, and h(x) = 2x. Find the exact value of each expression. Do not use a calculator. 4 93. + fl 6 94. + 6. 6 17 95. (h º g) 3 97. the average rate of change of f from 37 X1 = to x2 = 2 98. the average rate of change of g from = Ix to x2 = T 4

Exercises 97 and 98: Critical Thinking (Refer to Examples 9 and 10.) Use the given f(x) to complete the following. (a) Calculate the average rate of change of f from x = 1 to x = 2. (b) Illustrate your result from part (a) graphically. 97. f(x) = x² 98. f(x) = 4 – x²

How do I find the derivative of this equation ?