The Goal

Find

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.)