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# eeek, i've totally forgotten how to do directional derivatives! watch

1. two examples i've got here:

f(x,y,z)= x^2 - y^2 - 2zx

= 2(x-z)i - 2yj - 2xk

and

f(x,y,z)= ln(xy^2) + ln(y^2z) + ln(x^2z)

= 3lnx + 4lny + 2lnz

i know i have to derive but i've totally forgotten the rules- i don't know how to come to these conclusions! any help? thank you!
2. In general, .

So, for the "i" component of the first one, .

The 2nd one isn't a directional derivative, it's just using normal log rules (log(ab) = log(a)+log(b), log(a^n) = n log a).
3. (Original post by DFranklin)
In general, .

So, for the "i" component of the first one, .

The 2nd one isn't a directional derivative, it's just using normal log rules (log(ab) = log(a)+log(b), log(a^n) = n log a).
ahh thank you!! why didn't they do a directional derivative with the logs? is it not possible? and would i do it this way with any other kind of question i.e. sin, cos etc, or would they use the directional derivative formula? thank you!
4. Sure it's possible. I think what you posted is just the first line in a solution. They've simplified it using log rules. But then you just need to use the same method as for the first one.
5. oh my god, i've got it. thank you thank you!

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Updated: August 5, 2009
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