To find: The derivative of the function .
The derivative of is .
The function is .
(1) Difference Rule:
(2) Power Rule:
Obtain the derivative of .
Apply the difference rule (1),
Apply the power rule (2) and simplify further,
Therefore, the derivative of is .
To check: The derivatives of obtained in part (a) is reasonable or not by using the graphs of and .
The derivatives of is reasonable.
Use the online graphing calculator and draw the graph of and as shown below in Figure 1.
From Figure 1, it is noticed that,
If is positive then is increasing function.
If is negative then is decreasing function.
If crosses the x axis , then is local extrema (that is, local minimum or local maximum).
Therefore, it can be concluded that the derivative of the function is reasonable.
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!