Identity Sheet
The following is a list of definitions and formulas provided throughout the semester. The number of stars (*) represent how important the formula is to remember.
Identities and Definitions:
Definitions: \( \sinh(x) = \frac {1}{2} (e^x - e^-x) \) \( \cosh(x) = \frac {1}{2} (e^x + e^-x) \) \( \tanh(x) = \frac {sinh}{cosh} \) \( \coth(x) = \frac {1}{tanh(x)} \) \( sech(x) = \frac {1}{cosh(x)} \) \( cosech(x) = \frac {1}{sinh(x)} \) Identities: \( a^2 +b^2 = (a+b)(a-b) \) \(cosh^2(x) - sinh^2(x) = 1 \) \(\cosh(x + y ) = \cosh(x) \cosh(y ) + \sinh(x) \sinh(y) \) \(\sinh(x + y ) = \sinh(x) \cosh(y ) + \cosh(x) \sinh(y) \) \(\cosh(-x) = \cosh(x) \) \(\sinh(-x) = \sinh(x) \) \( \sinh(2x) = 2\sinh(x) \cosh(x) \) \( \cosh(2x) = \cosh^2(x) + sinh^2(x) = 1 + 2\sinh^2(x) = 2\cosh^2(x) -1 \) Table of Derivatives: |
Formula:
The Limit Definition: \( \lim_h\rightarrow0 = \frac {(t+h)^2 - t^2}{h} \) The Product Rule: \( (uv)' = u'v + v'u \) The Quotient Rule: \( (\frac {u}{v} = \frac {vu' - uv'}{v^2} \) The Chain Rule: Implicit Differentiation: \( \frac {d}{dx} = \frac {dy}{dx} \frac {d}{dy} \) The Quadratic Formula: \( \frac {-b \pm \sqrt{b^2 - 4ac}}{2a} \) L'Hopitals Rule |