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
Explorer

... Everest, (1790-1866) F Matthew Flinders, (1774-1814), first to circumnavigate Australia and Tasmania, extensively charted the coastline and named such features ...

 
 
 
This page was created in 24.2 ms