# Computing Derivatives

### Topics

## Introduction to Computing Derivatives - At A Glance:

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})

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