Problem 1
What is the name of the rule which states that \(\frac{d}{d x}\left(x^{n}\right)=\) \(n x^{n-1},\) where \(n>0\) is an integer?
Problem 1
\(\mathrm{T} / \mathrm{F}:\) The Product Rule states that \(\frac{d}{d x}\left(x^{2} \sin x\right)=2 x \cos x\).
Problem 1
What is the instantaneous rate of change of position called?
Problem 1
T/F: Let \(f\) be a position function. The average rate of change on \([a, b]\) is the slope of the line through the points \((a, f(a))\) and \((b, f(b))\).
Problem 1
T/F: The Chain Rule describes how to evaluate the derivative of a composition of functions.
Problem 1
In your own words, explain the difference between implicit functions and explicit functions.
Problem 2
T/F: The definition of the derivative of a function at a point involves taking a limit.
Problem 2
Given a function \(y=f(x)\), in your own words describe how to find the units of \(f^{\prime}(x)\).
Problem 2
Implicit differentiation is based on what other differentiation rule?
Problem 2
What is \(\frac{d}{d x}(\ln x) ?\)
