Question

what is the derivative of cosxcotx+sinx

Answer 1

use the product rule for the first part

Answer 2

let y=cos x cot x+sin x
\[y=\cos x \frac{ \cos x }{ \sin x }+\sin x=\frac{ \cos ^2x+\sin ^2x }{ \sin x }=\frac{ 1 }{\sin x }=\csc x\]
diff. w.r.t. x
\[\frac{ dy }{dx }=?\]

Answer 3

-cscxcotx
I like the simplification. Without simplifying, my answer is 2cosx-cotx/sinx.