derivative of ((x^2)+4)^x

Question

fibonaccichick666 · Answer

that's gonna be gross, ok, are you familiar with the chain rule?

thanatos2154 · Answer

Yes.

fibonaccichick666 · Answer

so, if you let $$x^2+4=u$$ what is the derivative of that part?

fibonaccichick666 · Answer

what is du?

fibonaccichick666 · Answer

u'

thanatos2154 · Answer

The derivative of u^x would be u^x right? No chain rule necessary.

fibonaccichick666 · Answer

not yet

fibonaccichick666 · Answer

first, we need du

fibonaccichick666 · Answer

since, we have an exponent on a function

thanatos2154 · Answer

I got as far as ln((x^2)+4)*(((x^2)+4)^x)

thanatos2154 · Answer

But i looked it up on wolfram alpha, and it had some extra.

fibonaccichick666 · Answer

That is not the derivative of the u I have defined.

fibonaccichick666 · Answer

we will need it eventually, and it is easier to just not have to write all of that out so a substitution makes our lives easier

thanatos2154 · Answer

Oh, ic. u' is 2x. right?

fibonaccichick666 · Answer

good, ok so now we can say, we have $u^x=f(x)$, you are correct that we will want to work with logs here to remove the exponent.  So, which log is convenient to take in order to move the x down?

thanatos2154 · Answer

ic, i normally use ln, my teacher says it doesn't matter.

fibonaccichick666 · Answer

yep, it's convenient to work with so I prefer it as well, so now, remember you must take the ln of both sides, then differentiate, can you please show your steps here.  (I can check for any misunderstandings this way)

fibonaccichick666 · Answer

you can go step by step posting so I can nip any issues in the bud

thanatos2154 · Answer

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