Derivatives of Exponential and Logarithmic Functions Notes 3.9 Derivatives of Exponential and Logarithmic Functions

I. Exponential Functions A.) Def. - B.) Inverse Functions:

II. Properties of Logarithms Given r > 0 and s > 0, A.) B.) C.) D.) E.)

III. y = ex

III. Derivatives A.)

B.)

C.)

D.)

IV. Logarithmic Differentiation A.) Complicated Form: Any form of equation with an xin both the base and the exponent. In order to take the derivative of functions in complicated form, we must take the log of both sides and then differentiate with respect to x.

B.) Find the derivative for each of the following using logarithmic differentiation.