Question

How do you find the second derivative of `h(x)=ln(2x^2+1)` ?

Answer 1

`=(4-8x^2)/((2x^2+1)^2)`

Explanation:

We use the chain rule to compute the derivative.

`(dh)/(dx) = (dh)/(du)(du)/(dx)`

`1/(2x^2+1)*4x = (4x)/(2x^2+1)`

Now we need to use the quotient rule.

`(d^2h)/(dx^2) = (4(2x^2+1) - 16x^2)/((2x^2+1)^2)`

`=(4-8x^2)/((2x^2+1)^2)`