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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