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

1 Answer
Dec 7, 2016

Answer:

#(-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)#