Question

how do you differentiate y=x(sqrt(1+x^2))?

Answer 1

you can use the product rule
and the chain rule to differentiate the term in the parentheses

Answer 2

write this part as (1 + x^2)^(0.5)

Answer 3

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

Answer 4

i'm not sure if i did it right

Answer 5

no
1/2 (1 + x^2)^ (-1/2) * 2x

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

Answer 6

- thats the derivative of the term in brackets

Answer 7

ohhh i see thanks

Answer 8

applying the product rule we get
x^2(1 + x^2)^(-1/2) + (1 + x^2)^(1/2)

Answer 9

we can convert this to 1 fraction if you like


= x^2 + 1 + x^2 1 + 2x^2
----------- = ------------
sqrt(1 + x^2) sqrt(1 + x^2)