**2.3.1. The power rule**

\(\frac{\mathrm{d}}{\mathrm{d}x} x^n = nx^{n-1}\)

You should be able to differentiate the following types for function

**power functions**like \(x^4\)**exponential**functions like \(e^{3x+2}\)**logarithm**functions like \(\ln(5x+7)\)

- the
**sum rule**(for addition) - the
**product rule**(for multiplication) - the
**quotient rule**(for division) - the
**chain rule**(for functions of functions)

Our recommendation is to:

**Test your ability by trying the diagnostic quiz**. You can reattempt it as many times as you want and can leave it part-way through.**Identify which topics need more work.**Make a note of any areas that you are unable to complete in the diagnostic quiz, or areas that you don't feel comfortable with.**Watch the tutorials for these topics,**you can find these below. Then try some practice questions from the mini quiz for that specific topic. If you have questions, please ask on the forum.**Re-try the diagnostic quiz.**And repeat the above steps as necessary until you can pass the diagnostic test. A pass grade is 80%.

Optionally, also see if you can **apply these skills to an economic application **or look at the **additional resources** and **advanced quizzes **at the bottom of the page,

\(\frac{\mathrm{d}}{\mathrm{d}x} x^n = nx^{n-1}\)

\(\frac{\mathrm{d}}{\mathrm{d}x} e^{ax} = ae^{ax}, \frac{\mathrm{d}}{\mathrm{d}x} \ln{(ax+b)} = \frac{a}{ax+b}\)

\(\left(\frac{u}{v}\right) = \frac{u'v-v'u}{v^2}\)

\(\frac{\mathrm{d}}{\mathrm{d}x} f(g(x)) = f'(g(x)) g'(x)\)

Differentiate more complicated functions by combining the rules above.

Producing output is costly and the relationship between the quantity produced and the cost of production is described by a producer's * cost function* . On the other hand by producing and selling output the producer realizes revenue and the relationship between the quantity produced and the revenue is described by a producer's

You can find **practice quizzes on each topic **in the links above the tutorial videos, or you can take the **diagnostic quiz **as many times as you like to If you want to test yourself further, then try the **advanced quiz** linked below.