Question

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

Answer 1

`(sinx -(x-2)cosx)/(sin^2x)`

Explanation:

differentiate using the`color(blue)" quotient rule "`

If f(x) `= (g(x))/(h(x))" then " f'(x) =( h(x).g'(x) - g(x).h'(x))/(h(x))^2`
`"------------------------------------------------------------------------"`

g(x) = x - 2 `rArr g'(x) = 1`

h(x) =`sinx rArr h'(x) = cosx`
`"--------------------------------------------------------"`
substitute these values into f'(x)

`rArr f'(x) = (sinx.1 - (x-2)cosx )/(sin^2 x)`