# At a Glance - More Derivatives of Logarithms

Whenever possible, rewrite a function so it looks good *before* taking its derivative.

Any logarithm log* _{b }a* can be written as

This allows us to find derivatives of logarithms in bases besides *e*.

We also know enough now to find derivatives of things like

*f*(*x*) = ln (*x*^{2}).

We can bring down the exponent to find

*f*(*x*) = 2 ln* x*,

and we know how to find the derivative of this:

#### Example 1

Find the derivative of |

#### Example 2

Find the derivative of |

#### Exercise 1

Find the derivative of the function.

*f*(*x*) = log_{9}*x*

#### Exercise 2

Find the derivative of the function.

*g*(*x*) = log_{2}*x*

#### Exercise 3

Find the derivative of the function.

*h*(*x*) = ln*x*^{10}

#### Exercise 4

Find the derivative of the function.

*j*(*x*) = log_{4 }*x*^{4}

#### Exercise 5

Find the derivative of the function.

*k*(*x*) = log_{5}(*x*^{3})