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Ok, so the problem problem probably isn't as bad as I'm making it, either that or its because its getting late & my brain just isn't functioning.

Find the derivative of y with respect to r.

y=[tex]log _2 \left( r \right)[/tex] * [tex]log _4 \left( r \right)[/tex]

The first thing I thought to do was use the product rule which yielded

y'=[tex]log _2 \left( r \right)[/tex]*(1/ln2)(1/r)+[tex]log _4 \left( r \right)[/tex](1/ln4)(1/r)

I then changed the [tex]log _2 \left( r \right)[/tex] to (ln r/ln2) & did the same to the other logarithm which created a complex fraction that I condensed down to

(ln r)/(r ln 2 * ln 2) + (ln r)/(r ln 4 * ln 4)

Cross multiplying gave

[(ln r)(ln 4)^2+ (ln r)(ln 2)^2]/[r (ln 2)^2 (kn 4)^2]

Here is where I'm stuck, because the book likes (2 ln r)/(r ln 2 * ln 4).

The book also showed different steps. To begin with it shows making the logs into ln.

which gives

y=(ln r)^2/(ln 2 * ln 4)

then take the derivative, but here is where I'm a bit lost. It shows

y'=1/(ln2 *ln 4) * (2 ln r) * (1/r)

I can see where the (2 ln r) & the (1/r) come from the chain rule, but not so much the 1/(ln2 *ln 4) part.

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# Homework Help: Derivative with logarithms

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