Unsure how to treat y in this derivative/log problem

Question

Need to find the derivative of $h(y)= \ln(y^2 \cos y)$

Treating it like a normal variable like an x isn't working for me, the way we used y's in earlier problems where you get a y' in there doesn't seem right, so I'm not quite sure here.

Answer 1

Mathematics is invariant under change of notation

Mathematics is invariant under change of notation

Mathematics is invariant under change of notation

You're doing something wrong if you treat that $y$ as differently than if it was an $x$ or a $\mu$ or small drawing of a house.

$$\frac{d}{dy}h(y)=\frac{2}{y}-\tan(y)$$ holds just as surely as it would if $y$ were $x$.

Answer 2

If $h(y) = \ln(y^2 \cos y)=2 \ln y + \ln(\cos y)$, then $$ h'(y) = \frac{2}{y} + \frac{-\sin y}{\cos y} = \frac{2}{y} - \tan y $$

Stella is right. In this problem, $y$ is an independent variable. You may have worked other problems where $y$ was dependent on $x$, but this is not the case here.