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

Question

asked Jan 19, 2022 92.4k views

1 Answer

JRI · Answer 1 · 2022-01-25T20:44:41+0000

Answer:

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