`(1)/(2)x^(2)-sqrt(11)x+1=0`

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

Evaluate the following limits : Lim_(x to 0 ) (sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1-x^(2))-sqrt(1-x))

lim_(xrarr0) (sqrt(1-x^(2))-sqrt(1+x^(2)))/(2x^(2))

Identify the curve sqrt((x+1)^(2)+y^(2))+ sqrt(x^(2)+(y-1)^(2))-2 =0

tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

The number of irrational solutions of the equation sqrt(x^(2)+sqrt(x^(2)+11))+sqrt(x^(2)-sqrt(x^(2)+11))=4 , is

Evaluate: int_0^(1/(sqrt(2)))(sin^(-1)x)/((1-x^2)sqrt(1-x^2))dx

Evaluate: int_0^(1/(sqrt(2)))(sin^(-1)x)/((1-x^2)sqrt(1-x^2))dx

Differentiate the following function (sqrt(x^2+1)+sqrt(x^2-1))/(sqrt(x^2+1)-sqrt(x^2-1)

Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))} with respect to cos^(-1)x^2