2.3 Product and quotient rules; question 58

[Eigenvalue]

Differentiate using the product and quotient rules:

f(x)=[tex]\frac{sin(x)}{1-cos(x)}[/tex]

[Eigenvalue]

f'(x)=[tex]\frac{cos(x)(1-cos(x))-sin(x)sin(x)}{(1-cos(x))²}[/tex]

=[tex]\frac{cos(x)-cos²(x)-sin²(x)}{(1-cos(x))²}[/tex]

=[tex]\frac{cos(x)-1}{(1-cos(x))²}[/tex]

=[tex]\frac{-1}{1-cos(x)}[/tex]