Common Calculus Mistakes
Chain Rule: Natural Logarithm

The Goal

Find

goal

where k and S0 are constants.


The Mistake

Find the mistake:

mistake

(Roll the mouse over the math to see a hint in red)


The Correction

correction

(Roll the mouse over the area above to see the correction in blue)


An Explanation

The chain rule is applied to the natural logarithm of a function g(x) as follows:

formula

In this example g(x) = S/S0, so the first part of the derivative should be 1/(S/S0) and this should be multiplied by g'(x) = 1/S0 (think of S/S0 as the constant 1/S0 times S).

(In the mistake the student did successfully find g'(x), apparently using the quotient rule to get S0/S02, which makes the derivative harder than necessary. For this reason that part of the mistake is also marked in red.)

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