Differential Calculus - Higher Order Derivatives

Kamis, 25 Juni 2020

Higher Order Derivatives

 

Function: f, y, u, v

Independent variable: x

Natural number: n

 

• Second derivative

     

• Higher-Order derivative

     

• (u + v)⁽ⁿ⁾ = u⁽ⁿ⁾ + v⁽ⁿ⁾

• (u – v)⁽ⁿ⁾ = u⁽ⁿ⁾ –  v⁽ⁿ⁾

• Leibnitz’s Formulas

   (uv)’’ = u’’v +2u’ v’ + uv’’

   (uv)’’’ = u’’’v +3u’’ v’ + 3u’v’’ + uv’’’

     

• 
• (xⁿ) = n!

• 
• 
• (a^x)⁽ⁿ⁾ = a^x lnⁿ a
• (e^x)⁽ⁿ⁾ = e^x
• (a^mx)⁽ⁿ⁾ = m^x a^mx lnⁿ a
• 
• 

Sumber

Labels: Mathematician

Thanks for reading Differential Calculus - Higher Order Derivatives . Please share...!