Question

Find the derivative of the function using the product rule (x)(sqrt(x^2+5))

Answer 1

u'v+uv'

Answer 2

you'll need the chain rule for the sqrt(x^2+5) term as well

Answer 3

\[\sqrt{{x ^2}+5}+x ^{2}/\sqrt{x ^{2}+5}\]

Answer 4

yep that looks right

Answer 5

i got that but can i simplify it anymore?

Answer 6

yeah you can multiply top and bottom by sqrt(x^2+5)

Answer 7

the first term I mean

Answer 8

(2x^2+5)/(sqrt(x^2+5))

Answer 9

i mean i have to substitute my x in for the equation of the tangent line is it a good idea to just leave that like that?

Answer 10

less computation if you simplify it a little further

Answer 11

\[x ^{2}/\sqrt{x ^{2}+5}\]so i added it and got

Answer 12

sorry 2x^2 +5 for numerator

Answer 13

sorry 2x^2 +5 for numerator