Choose the correct derivative of `sqrt x[1/(2sqrt x),-1,2sqrt x,x^1/2]`.

Choose the correct answer int sqrt(1+x^2) d x is equal to A) x/2 sqrt(1+x^2)+1/2 log |x+sqrt(1+x^2)|+C B) 2/3(1+x^2)^(3 / 2)+C C) 3/2 x(1+x^2)^(3 / 2)+C D) x^2/2 sqrt(1+x^2)+1/2 x^2 log |x+sqrt(1+x^2)|+C

The anti derivative of sqrt(x)+1/sqrt(x) is a) 1/3 x^(1/3)+2 x^(1/2)+C b) 2/3 x^(2/3)+1/2 x^2+C c) 2/3 x^(3/2)+2 x^(1/2)+C d) 3/2 x^(3/2)+1/2 x^(1/2)+C

x=1/(sqrt2+1) Find x+1/x

The derivative of tan^-1 ((2x)/(1-x^2)) with respect to cos^-1 sqrt(1-x^2) is a) (sqrt(1-x^2))/(1+x^2) b) 1/sqrt(1-x^2) c) 2/(1+x^2) d) (2sqrt(1-x^2))/(1+x^2)

Consider the function f(x)=sin^(-1)(2xsqrt(1-x^2)),(-1)/sqrt2lexle1/sqrt2 Show that f(x)=2sin^-1x

Evaluate int 1/(sqrt (x^2+2x+2))dx