Chapter 2: Q. 57 (page 222)
Use logarithmic differentiation to find the derivatives of each of the functions in Exercises 49–58.
Short Answer
The derivative of function is
Chapter 2: Q. 57 (page 222)
Use logarithmic differentiation to find the derivatives of each of the functions in Exercises 49–58.
The derivative of function is
All the tools & learning materials you need for study success - in one app.
Get started for freeEach graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
Taking the limit: We have seen that if f is a smooth function, then This approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.
.
Use the limit just defined to calculate the exact slope of the tangent line toat
If Katie walked at miles per hour for minutes and then sprinted at miles an hour for minutes, how fast would Dave have to walk or run to go the same distance as Katie did at the same time while moving at a constant speed? Sketch a graph of Katie’s position over time and a graph of Dave’s position over time on the same set of axes.
A bowling ball dropped from a height of feet will be feet from the ground after seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
When the bowling ball is first dropped, with
In Exercises 69–80, determine whether or not f is continuous and/or differentiable at the given value of x. If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
What do you think about this solution?
We value your feedback to improve our textbook solutions.