Find the derivative of the function

First, we take the logarithm of both sides so we can use logarithmic differentiation,

Then we differentiate both sides,

Therefore,

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Stumbling Robot

A Fraction of a Dot
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Find the derivative of *(x*^{2}(3-x)^{1/3})/((1-x)(3+x)^{2/3})

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Find the derivative of the function

First, we take the logarithm of both sides so we can use logarithmic differentiation,

Then we differentiate both sides,

Therefore,

This doesn’t address the issue of when , which it is, on the interval , in which case is not defined.

And also when .

I think they should’ve taken absolute value, log(|f(x)|), in which case everything seems to work out fine (since derivative of log(|f(x)|) is always 1/x).

I got (1/3)log(3-x)=-1/(3*(3-x)), but you seem to be saying (1/3)log(3-x)=+1/(3*(3-x)). Therefore, I am confused.