Section 3.3

Differentiation Formulas

Calculating limits every time is inefficient. Learn the "shortcuts" used by mathematicians.

1

Standard Formulas

The Power Rule

Bring the exponent down to the front, and subtract one from the new exponent.
This works for any real number , including fractions and negatives!

Constant Rule

Horizontal lines have 0 slope.

Sum/Difference Rule

Differentiation is linear:

2

Worked Example

Differentiate:

Apply Rules Term-by-Term
  • First term:
  • Second term:
  • Third term: (Constant)
Final Answer:
3

More Examples

Negative Exponents

Rewrite fractions first!

Problem:
Rewrite:
Differentiate:

Fractional Exponents (Roots)

Roots are just powers.

Problem:
Rewrite:
Differentiate:
5

Practice Quiz

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