Derivative sin ^2(x)/x^3

[nosit]

Hello,

I am trying to solve this derivative. I applied the quotient rule and in the last step I made I applied the chain rule in the first term (in the left).
Could someone please explain me the steps I should take to get the result?

This is what I've made:


And this is the result:

 

[pka]

Here is a PdF file of the steps.

 

[Dr.Peterson]

Hello,

I am trying to solve this derivative. I applied the quotient rule and in the last step I made I applied the chain rule in the first term (in the left).
Could someone please explain me the steps I should take to get the result?

This is what I've made:
View attachment 22396

And this is the result:

View attachment 22397

Your result is correct; they just simplified it further. They factored x^2 sin(x) from the numerator, then canceled the x^2 with the denominator.

It's important to be aware that simplification is not required. Many instructors I know tell students not to simplify, so that they can see whether the calculus is correct, without having to figure out whether an answer that has been simplified differently is equivalent to their own version.