How do you differentiate $f(x)=sinx/(1-cosx)$ ?

Question

8033 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-05T10:03:23

$(df)/(dx)=-1/(1-cosx)$

We use the quotient formula here. It states if $f(x)=(g(x))/(h(x))$

then $(df)/(dx)=((dg)/(dx)xxh(x)-(dh)/(dx)xxg(x))/(h(x))^2$

As $f(x)=sinx/(1-cosx)$

$(df)/(dx)=(cosx xx(1-cosx)-sinx xxsinx)/(1-cosx)^2$

= $(cosx-cos^2x-sin^2x)/(1-cosx)^2$

= $(cosx-(cos^2x+sin^2x))/(1-cosx)^2$

= $(cosx-1)/(1-cosx)^2$

= $-(1-cosx)/(1-cosx)^2$

= $-1/(1-cosx)$

How do you differentiate f(x)=sinx/(1-cosx)f(x)=sinx/(1-cosx)?