Question

Differentiate with respect to x:y= sinh^-1(x^2+1)

Answer 1

The first derivative of
`y = \sinh^(-1) (x^(2)+1)` is
`y' = \frac{2\cdot x}{\sqrt{x^(2)+2\cdot x +2}}`.

Explanation:

We proceed to find the first derivative of
`y = \sinh^(-1) (x^(2)+1)` by explicit differentiation and rule of chain:

`y = \sinh^(-1) (x^(2)+1)`

`y' = \frac{2\cdot x}{\sqrt{(x^(2)+1)^(2)+1}}`

`y' = \frac{2\cdot x}{\sqrt{x^(2)+2\cdot x +2}}`

The first derivative of
`y = \sinh^(-1) (x^(2)+1)` is
`y' = \frac{2\cdot x}{\sqrt{x^(2)+2\cdot x +2}}`.