calculus-derivatives?
give the indicated derivative:
d/dx (xsinx + x^2)/(x^2+1)
I just wanted to compare my final answer, i have used the product rule, within the quotient rule and came up with
(xsinxcosx +2x)(x^2+1) - (xsinx +x^2)(2x)/ (x^2 +1)^2
am I on the right track?
Comments
k = d/dx (x sin x + x^2)/(x^2+1)
k = [(sin x + x cos x + 2x)(x^2+1) - (x sin x + x^2)(2x)] / (x^2+1)^2
k = (x^3 cos(x)-x^2 sin(x)+2 x+sin(x)+x cos(x)) / (x^2+1)^2
You are definitely on the right track in that you should be using the quotient rule and you will need to use the product rule while doing so. The only problem I see is that you appear to have done the product rule incorrectly.
The derivative of the numerator is not xsinxcosx +2x
it should be sinx+xcosx+2x
You get that because you should do:
sinx*d/dx(x)+x*d/dx(sinx)+d/dx(x^2)
Yes you are right and close to the final result since there is not much left to simplify.
Listen to brian, or you could also use wolframalpha if you are just trying to check your work
You should listen to Brian
.
brians right