Question

How do you differentiate `f(x)=sec(1/sqrtx )` using the chain rule?

Answer 1

`(-1/2) (1/x^(3/2)) sec (1/sqrt x) tan(1/sqrt x)`

Explanation:

let `1/sqrt x` be 'p' which is obviously be a function of x. Thus sec (p) is to be differentiated w.r.t to x, that is to find out `d/dx sec p`.

The chain rule now becomes applicable as follows:

`d/dx sec p = d/(dp) sec p * d/dx p`

= `sec p tan p* d/dx (1/sqrtx)`

= `sec (1/sqrt x) tan(1/sqrt x)* (-1/2 x^(-3/2))`

=`(-1/2) (1/x^(3/2)) sec (1/sqrt x) tan(1/sqrt x)`