Question

what is the derivative of x*(sqrt(x^2+1))

Answer 1

x/2 * (x^2+1)^(-1/2) * (x^2+1)^(1/2)

Answer 2

\[(2x ^{2}+1)/\sqrt{x ^{2}+1}\]

Answer 3

i thought you were supposed to take the natural log of both sides?

Answer 4

no, product rule (uv)' = u'v+uv'

Answer 5

my instructions say use logarithmic differentiation. i got the answer:
\[(dy/dx)=[x \sqrt{x^2+1}][2+(1/2)\ln (x^2+1)]\]