" Example "10" lod "f(x)=(x)/(sqrt(1+x^(2)))" Then,show that "(tan" op ")(x)=(x)/(sqrt(1+3x^(2)))

Show that : tan (cos^(-1)x) = (sqrt(1-x^(2)))/x

If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))) , then show that (dy)/(dx) = x/(sqrt(1 - x^4))

If y="tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) show that, (dy)/(dx)=(x)/(sqrt(1-x^(4)))

If y = tan^(-1) ((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) show that (dy)/(dx) = x/sqrt(1-x^4) .

f(x)=sqrt(x^(2)+1) then lim_(xto3)(f(x)-sqrt(10))/(x-3) is

f(x)=2x-tan^(-1)x-ln(x+sqrt(1+x^(2)));x in R then

f(x)=sqrt(1-sin^(2)x)+sqrt(1+tan^(2)x) then

f(x)=sqrt(1-sin^(2)x)+sqrt(1+tan^(2)x) then

f(x)=sqrt(1-sin^(2)x)+sqrt(1+tan^(2)x) then