How do you differentiate y=sec^-1(x^2)y=sec1(x2)?

1 Answer
Jan 4, 2017

(dy)/(dx)=2/(xsqrt(x^4-1))dydx=2xx41

Explanation:

y=sec^(-1)x^2y=sec1x2

=>x^2=secyx2=secy

differentiate wrt xx

2x=(dy)/(dx)secytany2x=dydxsecytany

(dy)/(dx)=(2x)/(secytany)dydx=2xsecytany

now substitute back using:

secy=x^2secy=x2

sec^2y=1+tan^2y=>tany=sqrt(sec^2y-1sec2y=1+tan2ytany=sec2y1

tany=sqrt(x^4-1)tany=x41

(dy)/(dx)=(2x)/(x^2sqrt(x^4-1))=2/(xsqrt(x^4-1))dydx=2xx2x41=2xx41