Verify my differentiation of sinx / (x^2 + tanx)

[hank]

Differentiate: sinx / (x^2 + tanx)

I just want to verify my answer, which is:

(x^2 * cosx + cosxtanx - 2xsinx - sinxsec^2x) / (x^2 + tanx)^2

Does that look right? Thank you!

 

[skeeter]

looks fine ... I would have left it as

\(\displaystyle \L \frac{\cos{x}(x^2 + \tan{x}) - \sin{x}(2x + \sec^2{x})}{(x^2 + \tan{x})^2}\)

there's not much to gain by distributing the factors in the numerator.

 

[hank]

Thanks tons.

It just looked kind of weird to me for some reason.