Question

determine the derivative of f(x)=arctan x

Answer 1

@Vocaloid

Answer 2

Thsi is what I have so far

Answer 3

All the way up to df/x = 1/sec^2(x) is good

From there use a trig identity to rewrite sec(f) in terms of tan(f)

Then since f = arctan(x) then x = tan(f) so you can replace tan(f) with x

Answer 4

sin/cos ?

Answer 5

sec^2(theta) = 1 + tan^2(theta)

Apply this logic to your denominator

Answer 6

denominator as in sec^2(f)

Answer 7

Yes

Answer 8

ec^2(f) = 1 + tan^2(f)

Answer 9

and then it would condense down to

Answer 10

arctan x ?

Answer 11

Good

Then as we stated before, tan(f) = x so plug that in for tan^2(f) to get th final derivative

Answer 12

sec^2(f) = 1 + tan^2(x)

Answer 13

Your new denominator is 1 + tan^2(f)

Replacing tan(f) with x gives us

1 + x^2 as the new denominator

Answer 14

And that’s it, the derivative is 1/(1+x^2)

Answer 15

Anyway I can’t really stay but will try to be on later

Answer 16

SOunds good see you tonight