17-logs

17-logs - Math 1a Derivatives& Logarithms Fall 2009 1 In...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 1a Derivatives & Logarithms Fall, 2009 1 In this problem, we’ll figure out the derivative of ln( x ) and log a ( x ) (where a is a positive constant other than 1). We’ll do this in the same way we found the derivatives of arcsin( x ), arccos( x ), and arctan( x ) on Monday, as once again we’re dealing with an inverse function. (For example, arcsin( x ) is the inverse function of sin( x ): sin(arcsin( x )) = x for any x , and sin(arcsin( x )) = x for x in the interval [- π 2 , π 2 ].) (a) Write the equation y = ln( x ) in terms of only x , y , and e . (b) Differentiate the equation you found in part (a) implicitly and solve for dy dx . (c) Now write dy dx only in terms of x (and not y ). This is the derivative of ln( x ). (d) Repeat this process for the function y = log a ( x ), where a 6 = 1 is a positive constant. 2 Using the chain rule, we can expand the derivative rules you found to d dx (ln( u )) = 1 u du dx or d dx (ln( g ( x ))) = g ( x ) g ( x ) and d dx (log a ( u )) = 1 ln( a ) u du dx or d dx (log a ( g ( x ))) = g ( x ) ln( a ) g ( x ) Use these rules to differentiate the following: (a) ln(cos( x )) (b) ln( √ x )...
View Full Document

{[ snackBarMessage ]}

Page1 / 4

17-logs - Math 1a Derivatives& Logarithms Fall 2009 1 In...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online