Question

Find the derivative of `y=sinh^(-1)(1+x^2)`?

Answer 1

`(dy)/(dx)=(2x)/sqrt(x^4+2x^2+2)`

Explanation:

As `y=sinh^(-1)(1+x^2)`, we have `sinhy=1+x^2`

Hence `coshy=sqrt(1+(1+x^2)^2)=sqrt(x^4+2x^2+2)`

Taking derivative on both sides of `sinhy=1+x^2`

`coshy*(dy)/(dx)=2x`

i.e. `(dy)/(dx)=(2x)/sqrt(x^4+2x^2+2)`