# Differentiation of standard functions

## Summary and examples

In general the following derivatives of standard functions are assumed to be known.  a.  b.  c.  d.  e.  f.  g.  h.  Furthermore we have the following rules:

If:

i. then: and if:

j. then: In the following examples we show how these rules are applied.

##### Example 1 so: (according to a)

##### Example 2 so: (according to a, i)

##### Example 3 so: (according to c)

##### Example 4 so: (according to e, i)

##### Example 5 so: (according to f, i)

##### Example 6 so: (according to a, h, i, j)

##### Example 7 so: (according to a, f, i, j)

Now some more difficult examples.

##### Example 8

Find the derivative of: At first sight this function is not in the table of standard functions. However we can rewrite the function: and thus rule a. can be applied with: So: ##### Example 9

Differentiate: This function can be written as: and thus: (according to a,i)

##### Example 10

A difficult function seems: but also this function can be rewritten and be differentiated easily: and thus: (according to a, b, j)

##### Example 11

Differentiate the following function: We can rewrite the function as follows: and thus: (according to a, i)

##### Example 12

Finally we want to differentiate the following function: We can rewrite it as follows: The derivative is: 0