Question

How do you find the derivative of `y =cotx/(1-sinx)`?

Answer 1

Use the quotient rule:

If we let `cotx/(1-sinx)=f(x)/g(x)`

Then, to find the derivative using the quotient rule would generally look like:

`(f'(x)*g(x)-g'(x)*f(x))/g(x)^2`

Therefore, `y'` would look like:

`y'=[d/dxcotx*(1-sinx)-d/dx(1-sinx)*cotx]/(1-sinx)^2`

Find the derivatives and simplify.