Rules of differentiation

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After completing this section, students should be able to do the following.

Use the definition of the derivative to develop shortcut rules to find the derivatives of constants and constant multiples.
Use the definition of the derivative to develop shortcut rules to find the derivatives of powers of $x$ .
Use the definition of the derivative to develop shortcut rules to find the derivatives of sums and differences of functions.
Compute the derivative of polynomials.
Recognize different notation for the derivative.
State the derivative of the natural exponential function.
State the derivative of the sine function.