Review

Definition of the Derivative

f'(x) = \lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}{h}

The derivative at a point is the slope of the tangent line to the graph of the function at that point.

Derivative Formulas

Practice Exercises

Using the derivative formulas above, compute each of the following derivatives in questions 1-10. You may replace the letters serving as constants with your favorite numbers (a,b,c,d,e, and f) first if you wish. In particular, note that making some constants equal to one will greatly simplify the problem.

  1. y(x) = ax^b

  2. y(x) = \frac{ax^b + cx^d}{ex^f}

  3. y(x) = e^{ax^b}

  4. y(x) = \ln{ax^b}

  5. y(x) = \frac{a}{b + ce^{dx}}

  6. y(x) = ab^{cx}

  7. y(x) = a(b + cx^d)^e

  8. y(x) = \frac{ax^b + c}{dx^e + f}

  9. y(x) = (a + b\ln(cx))(d + e\ln(fx))

  10. y(x) = a

  11. If the units of x are input and the units of f(x) are output, what are the units of f'(x)?

Past Quizzes and Exams

Quiz

Solutions

LaTeX source

exam1.pdf

exam1-solutions.pdf

exam1.tex

exam2.pdf

exam2-solutions.pdf

exam2.tex

practice_exam.pdf

practice_solutions.pdf

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Questions

How do I ask a question?

NUWiki: Math1341 (last edited 2011-08-07 19:44:06 by JasonRibeiro)