Question

find the derivative h(x) = x2 arctan(4x)

Answer 1

wee need the product rule for this one.

Answer 2

so u'v + v'u

Answer 3

correct

Answer 4

2x * arctan(4x) + 4/1+4^2

Answer 5

so 2xarctan(4x) + \[\frac{1}{1+16}?\]

Answer 6

err 4/....

Answer 7

you forgot the x

Answer 8

16x^2 oopsies.

Answer 9

good
then as you said, 4/...

Answer 10

\[\frac{4}{1+16x^2}\]

Answer 11

times...?

Answer 12

*x^2

Answer 13

you got it :)

Answer 14

so that would be \[\frac{4x^2}{1+16x^2}\] can't we cancel out 4x^2 and 16X^2?

Answer 15

no, how would you do that?
if you divide top and bottom by 4x^2 you get something ugly...

Answer 16

okies :P You cannot split it up though either right? That's only the numerator?

Answer 17

you could split it up if you wanted with long division or partial fractions, but I see no point in that

Answer 18

okies...

Answer 19

so final answer is 2xtan(4x) + \[\frac{4x^2}{1+16x^2}\]

Answer 20

arctan*

Answer 21

yeah that :P. I fail haha.

Answer 22

it happens to us all :)

Answer 23

At first it said it was wrong, but I typed acr tan because I messed up at first typing artan and it turned art into something weird LOL :(