Florida B.E.S.T. MA.912.C.2.8
The Standard
Find derivatives using logarithmic differentiation.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students take the natural log of both sides and use log rules to rewrite powers, products, or quotients. They differentiate implicitly, solve for y', and replace y with the original function.
What Mastery Looks Like
- Students choose this method when variables appear in both the base and exponent or when products and quotients are cumbersome. They expand logarithms correctly, differentiate implicitly, isolate y', and substitute the original expression for y.
Common Misconceptions
- Students may apply the power rule while treating a variable exponent as constant. They also misuse log rules, omit the y'/y factor, or forget to solve for y' after differentiating.
How to Assess It
- Exit ticket: Find y' for y=(x²+1)^x. Show the log-law expansion and a simplified final answer.
Lesson moves
Ways to Teach It
Give students expression cards and log-law cards; they match each expression to its expanded logarithm, then differentiate and verify with a partner.
Ask: Why does taking ln help with y=(x+1)^x, and where does the y'/y term come from?
Run a three-problem relay where teams earn one point each for correct log expansion, implicit derivative, and solved derivative.
Use N(t)=t^t as a simplified sharing model, and have students find and interpret the instantaneous growth rate at t=2.
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