If `y = log ( x +sqrt(a^2+x^2))`, find `dy/dx`.

IF [y{sqrt(x^2 + 1)- log {1/x +sqrt(1+1/x^2)}] find dy/dx

Find dy/dx if y = log {2x + sqrt (4x^2 + a^2) } .

If y = (log x)^x + x^(log x) , then find dy/dx .

If y = f (log_e x) and f'(2) = 2 , find dy/dx at x = e^2

If y = log (x + sqrt(x^2+1))/(sqrt(x^2+1)) , prove that (x^2 +1) dy/dx + xy = 1

If y = log sqrt((1 + cos^2 x)/(1 - e^(2x))), find (dy)/(dx) .

If y= (sqrt(x) + 1/sqrt(x))^2 .Find dy/(dx)

Find (dy)/(dx) if y = log (x + 3 + sqrt(x^2 + 6x + 3))

Find (dy)/(dx) if y = log (sqrt(2x + sqrt(4x^2 + a^2)))

Find the second order derivative of the following functions If y = log[x + sqrt(x^2 + a^2)] , show that (x^2 + a^2) (d^2y)/(dx^2) + x (dy)/(dx) = 0