Hello! I am having trouble deriving ((3x/x^2+1))^4 by the chain rule. All I have written down is f'(x)= 4(3x/x^2+1)^3 * (-3x^2+3/x^4+2x^2+2)

I stopped because I didn't know what to do next or if that was the right track to go...Is there any easy way to do this problem?

Question

Hello! I am having trouble deriving ((3x/x^2+1))^4 by the chain rule. All I have written down is f'(x)= 4(3x/x^2+1)^3 * (-3x^2+3/x^4+2x^2+2)


I stopped because I didn't know what to do next or if that was the right track to go...Is there any easy way to do this problem?

zepdrix · Answer

On a problem like this, if you're able to get an answer in that form, it's a good place to stop. Don't try to simplify any further unless your teacher wants you to.

Now the question is whether or not you did the derivation correctly^^ let's see.

zepdrix · Answer

Hmm Yes, good work! :)

So I'm assuming you applied the quotient rule for the inside, you can even stop a step earlier. Don't expand the denominator (unless your teacher wants you to), it just looks better left as a square.

Good Job! :D

zepdrix · Answer

I think you get x^4+2x^2+1
Not +2

On the far right, minor detail though c:

zepdrix · Answer

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They simplified it further than this? ... yikes.. I dont like yer book XD