Question

I have the answer can someone please check me.....
Find the derivative of
h(x)=arctan(1/x)

Answer 1

h(x)=arctan(1/x)

Answer 2

yes

Answer 3

I got for the answer\[\frac{ x^2 }{ x^2+1}\]
is that correct

Answer 4

Yes it's correct.

Answer 5

ok thanks

Answer 6

keep in mind that the answer is negative though

Answer 7

since the derivative of the inner function 1/x is -1/(x^2)

Answer 8

wait I'm confused now then what should the answer look like

Answer 9

h(x) = arctan(1/x)

h ' (x) = d/dx [ arctan(1/x) ]

h ' (x) = 1/( (1/x)^2 + 1) * d/dx[ 1/x ]

h ' (x) = 1/( 1/x^2 + 1) * (-1/x^2)

h ' h(x) = (1/x^2)/( 1/x^2 + 1)

h ' (x) = -1/(1 + x^2) ... multiply every term by x^2 to clear out the fractions

Answer 10

So the answer is h ' (x) = -1/(1 + x^2) or h ' (x) = -1/(x^2 + 1)

Answer 11

ok got it thanks

Answer 12

yw