Split - 2nd Derivative Question

[kss]

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Find the second derivative of d(t) = t/(t^2+3)

I found the first derivative which is [-t^2+3]/[(t^2+3)^2]

The problem I'm having with this question is when I find the second derivative do I use the chain rule while I use the quotient rule?

I can't figure out if it is okay to use more than 1 rule on one function.

 

[stapel]

I found the first derivative which is [-t^2+3]/[(t^2+3)^2]
The problem I'm having with this question is when I find the second derivative do I use the chain rule while I use the quotient rule?

I can't figure out if it is okay to use more than 1 rule on one function.

It's always "okay" to use more than one rule for one derivative. In fact, the further you get, the more common will become the need!

 

[Quaid]

[-t^2+3]/[(t^2+3)^2]

do I use the chain rule while I use the quotient rule?

When differentiating a composite function, the Chain Rule is always needed.

You have a composite function, in the denominator.

(t^2 + 3)^2

That's the squaring function. But the input to the squaring function is itself another function.

In other words, the inner function is STUFF and the outer function is (STUFF)^2. The Chain Rule is needed to differentiate the composite function (STUFF)^2.

The derivative of STUFF^2 is 2*STUFF*STUFF'