Question

Differentiate: y=1+cosx/1-cosx

Answer 1

\[(\frac{1+\cos(x)}{1-\cos(x))})'=\frac{(1+\cos(x))'(1-\cos(x))-(1+\cos(x))(1-\cos(x))'}{(1-\cos(x))^2}\]

Answer 2

1+cosx/1-cosx = cot( x/2) now diffnciate it...

Answer 3

sorry cot^2(x/2)

Answer 4

\[(1+\cos(x))'=0-\sin(x) =-\sin(x)\]
\[(1-\cos(x))'=0-(-\sin(x))=+\sin(x)=\sin(x)\]
And I suppose we could had attempted simplifying before differentiating lol

Answer 5

\[-2\sin \chi \div \left( 1-\cos \chi \right)^{2}\]

Answer 6

??

Answer 7

\[\frac{-\sin(x)(1-\cos(x))-(1+\cos(x))(\sin(x))}{(1-\cos(x))^2}=\frac{\sin(x)(-(1-\cos(x)-(1+\cos(x))}{(1-\cos(x))^2}\]
\[=\frac{\sin(x)(-2)}{(1-\cos(x))^2}\]
yes thats right! :)