Common Calculus Mistakes
Chain Rule: Natural Logarithm

The Goal



where k and S0 are constants.

The Mistake

Find the mistake:


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

The 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:


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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