Question

How do you differentiate `f(x)=sec^2(3x )` using the chain rule?

Answer 1

`6sec^2(3x)tan(3x)`

Explanation:

differentiating using the `color(blue)" chain rule "`

`d/dx [f(g(x) ] = f'(g(x).g'(x)`

and the standard derivative : `d/dx(secx) = secx.tanx`
`" ----------------------------------------------------------"`

f(g(x) = `[sec(3x)]^2 rArr f'(g(x)) = 2sec(3x)`

and g(x) =`sec(3x) rArr g'(x) = sec(3x).tan(3x). d/dx(3x)`

`= 3sec(3x).tan(3x)`
`" ------------------------------------------------------"`

`rArr f'(x) = 2sec(3x). 3sec(3x).tan(3x)`

`= 6 sec^2(3x).tan(3x)`