Math 3A – Prof. Wittman Derivatives of Exponential & Logarithmic Functions xxeedxd= xxdxd 1ln = Differentiate the following functions. 1.) 262)(+=xexxf 2.) ()26ln)(2+= xxxg 3.) ()xxh tanln)( = 4.) xexjxln)( =Math 3A – Prof. Wittman Derivatives in Other Bases ( )xxbbbdxdln= ( )xbxdxdbln1log = Differentiate the following functions. 1.) 853)(−=xxf 2.) xxxgcos210)( = 3.) ++=135log)(22xxxh 4.) ()xxj 5log)(5= Can you explain the answer you get?Math 3A – Prof. Wittman Introduction to Logarithmic Differentiation Sometimes a function is so nasty we don't want to differentiate it. Consider ( )426831cos+=−xxeyx This would involve some very nasty quotient and product rules to differentiate. We can make our life a little easier by taking the natural log of both sides of the equation first. ( )+=−426831coslnlnxxeyx 1.) Use the properties of logarithms to simplify the right hand side. 2.) Now differentiate both sides of the equation. Note the left side is dxdyyydxd 1ln =. 3.) Finally solve the equation for dxdy, plugging in the original value of y in terms of