higher order derivatives of sine and cosine
One may consider the sine and cosine either as real (http://planetmath.org/RealFunction) or complex functions. In both cases they are everywhere smooth, having the derivatives of all orders (http://planetmath.org/OrderOfDerivative) in every point. The formulae
where (the derivative of the order means the function itself), can be proven by induction on . Another possibility is to utilize Euler’s formula, obtaining
here one has to compare the real (http://planetmath.org/ComplexFunction) and imaginary parts – supposing that is real.
|Title||higher order derivatives of sine and cosine|
|Date of creation||2013-03-22 14:45:16|
|Last modified on||2013-03-22 14:45:16|
|Last modified by||pahio (2872)|