Question

If y = log(x2√(x2 + 1)) then find dy/dx.

Answer 1

y = log(x2√(x2 + 1))

Differentiating w.r.t. 'x'

dy/dx = ((d log(x2√(x2 + 1)))/d(x2√(x2 + 2))) x ((d(x2√(x2 + 1)))/dx)

= (1/x2√(x2 + 1)) x ((dx2/dx) x √(x2 + 1) + (x2d√(x2 + 1)/dx))

= (1/x2√(x2 + 1)) x (2x√(x2 + 1) + x2 x (1/2√(x2 + 1)) x 2x)

= (1/x2√(x2 + 1)) x (2x√(x2 + 1) + (x2/√(x2 + 1)))