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5.1 Logarithmic, Exponential, and Other Transcendental Functions. -The best way to learn this, I personally think is to do them together and just see example after example, until you pick up on the patterns. General formula for when u = something more complicated than x.
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5.1 Logarithmic, Exponential, and Other Transcendental Functions -The best way to learn this, I personally think is to do them together and just see example after example, until you pick up on the patterns.
General formula for when u = something more complicated than x.
Use log properties to help differentiate Use log properties to separate, then use ln differentiation rule
Natural log of both sides Natural log property Differentiation rule for ln Substitute y back in
Take the ln of both sides • Sometimes it is beneficial to use logs to help differentiate something that is non-logarithmic to start with.
The natural log (ln) is undefined for negative numbers, so you will often see expressions in the form ln|u|. We can approach these problems as if the absolute value bars did not exist.
Differentiation of Exponential(2 CASES) Some texts refer to this as a indestructible function because the derivative does not get simpler In this situation a is some number other than zero, we want a to be greater than 1.
Product rule combined with exponential rule. Simple constant raised to a variable
When the exponent is more complicated like a whole separate function, we use the following formulas. These things may seem complicated but they are simply things we have to memorize, in addition we will have to use things like product rules, sum rules, quotient rules, etc.
