Question

Which derivative correctly represents differentiating \[\ln y\] carefully?

Options

• \[\frac{d}{dx}(\ln y)=y\frac{dy}{dx}\]

• \[\frac{d}{dx}(\ln y)=\frac{1}{y}\frac{dy}{dx}\]

• \[\frac{d}{dx}(\ln y)=\ln\left(\frac{dy}{dx}\right)\]

• \[\frac{d}{dx}(\ln y)=\frac{dy}{dx}\]

Answer 1

Because \[y\] is a function of \[x\], the chain rule is required. Therefore the derivative of \[\ln y\] is \[\frac{1}{y}\frac{dy}{dx}\].