Encyclopedia > Linearity of differentiation

  Article Content

Linearity of differentiation

Differentiation is a linear operator; this property of the derivative which follows from the sum rule in differentiation and the constant factor rule in differentiation.

Let f and g be functions. Now consider:

<math>{d \over dx}(af(x) + bg(x))</math>

By the sum rule in differentiation, this is:

<math>{d \over dx}(af(x)) + {d \over dx}(bg(x))</math>

By the constant factor rule in differentiation, this reduces to:

<math>af\ '(x) + bg'(x)</math>

Hence we have:

<math>{d \over dx}(af(x) + bg(x)) = af\ '(x) + bg'(x)</math>

Omitting the brackets[?], this is often written as:

<math>(af + bg)' = af\ '+ bg'</math>



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Thomas a Kempis

... in French in 1651. The "Imitation of Christ" derives its title from the heading of the first book, De imitatione Christi et contemptu omnium vanitatum mundi. I ...

 
 
 
This page was created in 60.1 ms