## 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: