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

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

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

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

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

If y = {x+sqrt (x^2 + a^2})^n , prove that dy/dx= (ny)/sqrt (x^2+a^2) .

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

IF y =[log (x+ sqrt(1+ x^2))]^2 ,show that (1+ x^2) (d^2y) /dx^2 +x(dy/dx) =0

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)), prove that: (x^2+1) d^2y/dx^2 + xdy/dx=0 .

If y = sqrt(((x-3)(x^2+4))/((3x^2 + 4x + 5)) , then find dy/dx