Question

How do you differentiate `f(x)= (1 - sin^2x)/(cosx-1)` using the quotient rule?

Answer 1

see below

Explanation:

`d/dx((1-sin^2(x))/(cos(x)-1))=d/dx((cos^2(x))/(cos(x)-1))`

`=>((cos(x)-1)*d/dx(cos^2(x))-cos^2(x)*d/dx(cos(x)-1))/(cos(x)-1)^2`

`=>(sin(x)*cos^2(x)-2*sin(x)cos(x)*(cos(x)-1))/(cos(x)-1)^2`

`=>(sin(x)cos(x)*(2-cos(x)))/(cos(x)-1)^2`