35*sin^(-1)(2ax^(-1))sqrt(1-a^(2)x^(2))}

Differentiate sin^(-1)(2ax sqrt(1-a^(2)x^(2))) with respect to sqrt(1-a^(2)x^(2)), if -1/(sqrt(2))

Differentiate sin^(-1) (2ax sqrt(1-a^2x^2)) wth respect to sqrt(1-a^2x^2) .

Differentiate sin^(-1)(2a xsqrt(1-a^2x^2)) with respect to sqrt(1-a^2x^2) , if -1/(sqrt(2)) < ax<1/(sqrt(2)) .

Differentiate sin^(-1)(2a xsqrt(1-a^2x^2)) with respect to sqrt(1-a^2x^2) , if -1/(sqrt(2)) < ax<1/(sqrt(2)) .

If x in[(sqrt(3))/(2), 1] then [sin^(-1){(x)/(sqrt(2))+(sqrt(1-x^(2)))/(sqrt(2))}-sin^(-1)x]=

If x in[-1/2,1] then sin^(-1)(sqrt(3)/(2)x-1/2sqrt(1-x^(2)))

If x in[-1/2,1] then sin^(-1)(sqrt(3)/(2)x-1/2sqrt(1-x^(2)))

(1)/(sqrt(ax-x^(2)))

What is lim_(xtooo) (sqrt(a^(2)x^(2)ax+1)sqrt(a^(2)x^(2)+1)) equal to?

Prove the following : sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,x in[-1/sqrt2,1/sqrt2]