Find dy/dx where y = (x^2 - 5)/(cos(x))
I used the quotient rule and got (Cos x)(2x)-(x^2-5)(-sinx)/(cosx)^2 = (2cosx^2 +sinx^3 + 5 sin x)/ ((cosx)^2)
Is it possible to break this down further algebraically?
Algebraically this can be reduced by some standard trigonomic identities. So we have:
$\displaystyle \frac{2cos(x^2)+sin(x^3)+5sin(x)}{cos(x)cos(x)}$
By splitting up the fractions we get the following:
$\displaystyle \frac{2cos(x^2)}{cos(x)cos(x)} + \frac{sin(x^3)}{cos(x)cos(x)} + \frac{5sin(x)}{cos(x)cos(x)}$
the last term in the above expression reduces to:
$\displaystyle 5sec(x)tan(x)$
Other then that I'm not sure how much more reducing can be done, but the post above mine gives a different technique for going about the differentiation that gives a simpler seeming answer, so thats an option too.