Differentiate
f
(
x
)
=
5
cot
−
1
(
x
3
)
\displaystyle {f{{\left({x}\right)}}}={5}{{\cot}^{{-{1}}}{\left(\frac{{x}}{{3}}\right)}}
f
(
x
)
=
5
cot
−
1
(
3
x
)
. Use exact values. You should simplify the complex fraction.
f
′
(
x
)
=
\displaystyle {f}'{\left({x}\right)}=
f
′
(
x
)
=
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