Question

How to find f '(a). f(x) = √ 2-6x ?

Answer 1

If `f(x) = sqrt( 2 - 6x)`

Define `h(x) = 2 - 6x`
and `g(x) = sqrt(x) = x^(1/2)`
so
`f(x) = g(h(x)`

Use the product rule:
`(d f(x))/(dx) = (d g(h(x)))/(d h(x)) * (d h(x))/(dx)`

`= ((1/2) * (2 - 6x)^(-1/2)) * (-6)`

`= (-3)/(sqrt(2-6x))`

So,
`f'(a) = (-3)/(sqrt(2-6a))`