Question

Differentiate the function: y=sqrt(xe)^x^2(x^2+1)^10

Answer 1

Hmmm. Kind of murky. In any case, it's just the chain and product rules.

y = √x e^(x^2) (x^2+1)^10

Recall that if y=uvw then
y' = u'vw + uv'w + uvw'

So, that would give us

y' = 1/(2√x) * e^(x^2) * (x^2+1)^10
+ √x * 2x e^x^2 * (x^2+1)^10
+ √x * e^x^2 * 10(x^2+1)^9*2x
= √x e^x^2 (x^2+1)^9 ((x^2+1)/(2x) + 2x(x^2+1) + 20x)

and you can massage that more if you like

If I got it wrong, then fix the syntax and show us whatcha got.