differentiation where am I going wrong

[fran1942]

Hello, I am trying to differentiate:
{-xsinx-cosx} / x^2

My attempt using product and quotient rules is:

(-1(sinx)+(-xcosx)+sinx) * (x^2)) - (-xsinx-cosx) * 2x) / x^4

= {-x^3cosx+2x^2sinx+2xcosx} / x^4

But I don't seem to be correct. Can anyone please see where I am going wrong ?
Thanks kindly

 

[tkhunny]

Did you simplfy it? There's a whole ot of 'x's going on in there. Might there be a common factor in numerator and denominator?

 

[HallsofIvy]

You might find it better to simplify at the start: (-x sin(x)- cos(x))/x^2= - sin(x)/x- cos(x)/x^2.

 

[Deleted member 4993]

I am assuming this is a contnuation of the thread:

http://www.freemathhelp.com/forum/threads/75318-determine-concavity?p=309625#post309625

If I were to do this problem I would do it the following way:

{-xsinx-cosx} / x^2

f(x) = - sin(x)/x - cos(x)/x²

f'(x) = -[x * cos(x) - sin(x)]/x² - [-x² * sin(x) - 2*x*cos(x)]/x⁴

Now simplify .......