Question

How do you find the derivative of `sinx/x`?

Answer 1

You can use the quotient rule or the product rule.

Quotient Rule
`h(x) = f(x)/g(x)`
`h'(x) = (g(x)*f'(x) - f(x)*g'(x))/((g(x))^2)`

`h(x) = sinx/x`
`h'(x) = (x*(sinx)' - sinx*(x)')/(x^2) = (xcosx - sinx)/x^2`
`= cosx/x - sinx/x^2`

Product Rule
`h(x) = f(x)*g(x)`
`h(x) = f(x)*g'(x) + g(x)*f'(x)`

`h(x) = 1/x*sinx`
`h'(x) = 1/x*(sinx)' + sinx*(1/x)' = cosx/x - (sinx)/x^2`

As you can see, you still get the same result in the end.