How do you differentiate $x^2sqrt(x^4+1)$ ?

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Answer 1 · 2017-03-05T09:25:36

$=(4x^5+2x)/(sqrt(x^4+1))$

Since

$f(x)=g(x)*h(x)->f'(x)=g'(x)*h(x)+g(x)*h'(x)$
and
$f(x)=sqrt(g(x))->f'(x)=1/(2sqrt(g(x)))*g'(x)$ ,

then

$y=x^2sqrt(x^4+1)->y'=2x*sqrt(x^4+1)+x^2*1/(cancel2sqrt(x^4+1))*cancel4^2x^3$

$=2x*sqrt(x^4+1)+(2x^5)/(sqrt(x^4+1))$

$=(2x*(x^4+1)+2x^5)/(sqrt(x^4+1))$

$=(4x^5+2x)/(sqrt(x^4+1))$

How do you differentiate x^2sqrt(x^4+1)x^2sqrt(x^4+1)?