Differentiation Error With Natural Logarithm

Question

A researcher models profit using the function $$P(x)=\ln(x)-0.1x$$, where $$x$$ represents thousands of units sold. To find the number of units that maximizes profit, the researcher differentiates $$P(x)$$ but incorrectly computes the derivative of $$\ln(x)$$ as $$\ln(x)$$ instead of $$\frac{1}{x}$$. Which statement best describes this error?

Accepted Answer

They misapplied the derivative of $$\ln(x)$$, confusing it with the function itself instead of using $$\frac{1}{x}$$ as the correct derivative.

Answer

They incorrectly differentiated the linear term by introducing an extra constant.

Answer

They failed to differentiate the $$-0.1*x$$ term entirely, leading to an incomplete derivative.

Answer

They applied the product rule where it was not required, complicating the derivative unnecessarily.

Differentiation Error With Natural Logarithm

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