" (ii) "(a^(2)+x^(2))/(sqrt(a^(2)-x^(2)))

Differentiate the following w.r.t.x. (sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)-x^(2))-sqrt(a^(2)-x^(2)))

Differentiate the following w.r.t.x. (sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)+x^(2))-sqrt(a^(2)-x^(2)))

Differentiate the following w.r.t.x. (sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)-x^(2))-sqrt(a^(2)-x^(2)))

Differentiate the following w.r.t.x. (sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)-x^(2))-sqrt(a^(2)-x^(2)))

If =(sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)+x^(2))-sqrt(a^(2)-x^(2))), show that (dy)/(dx)=(2a^(2))/(x^(3)){1+(a^(2))/(sqrt(a^(4)-x^(4)))}

int (sqrt(a^(2)-x^(2))+(x^(2))/(sqrt(a^(2)-x^(2))))dx

Evaluate the following limits : lim_(x to 0)(sqrt(a^(2)+x^(2))-sqrt(a^(2)-x^(2)))/x^(2).

Show that the segment of the tangent to the curve y=(a)/(2)In((a+sqrt(a^(2)-x^(2)))/(a-sqrt(a^(2)-x^(2))))-sqrt(a^(2)-x^(2)) contained between the y= axis and the point of tangency has a constant length.

If int sqrt(a^(2)-x^(2))dx=(x)/(2)sqrt(a^(2)-x^(2))+k sin^(-1)(x/a)+c , then the value of k is-

(d)/(dx ) {(sqrt(a^(2)+x ^(2))+ sqrt(a ^(2) -x ^(2)))/(sqrt(a ^(2) + x ^(2)) - sqrt(a ^(2) - x ^(2)))}=