Find the differentiation of y=cos^-1(ax)?

1 Answer
maganbhai P.
Apr 27, 2018

y=cos^-1(ax)=>(dy)/(dx)=-1/sqrt(1-(ax)^2)d/(dx)(ax)
(dy)/(dx)=-1/sqrt(1-a^2x^2)xxa=(-a)/sqrt(1-a^2x^2)
Note: color(red)(d/(dX)(cos^-1X)=-1/sqrt(1-X^2)

Explanation:

Here,

y=cos^-1(ax)

Let, u=ax=>(du)/(dx)=a

So, y=cos^-1u=>(dy)/(du)=-1/sqrt(1-u^2)

"Using "color(blue)"Chain Rule",

color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx)

:.(dy)/(dx)=-1/sqrt(1-u^2)xxa=(-a)/sqrt(1-u^2),where, u=ax

=>(dy)/(dx)=(-a)/sqrt(1-(ax)^2)

=>(dy)/(dx)=(-a)/sqrt(1-a^2x^2)

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