How do you differentiate $f(x)=2^cotx$ ?

Question

3986 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-05T20:30:04

$f'(x)=-2^cotxln2csc^2x$

use logarithmic differentiation

let $" "y=2^cotx$

$=>lny=cotxln2$

differentiate wrt $x$

$1/y(dy)/(dx)=- csc^2xln2$

$(dy)/(dx)=-yln2csc^2x$

substitute back for $y$

$f'(x)=-2^cotxln2csc^2x$

How do you differentiate f(x)=2^cotxf(x)=2^cotx?