Question

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

Answer 1

Answer:

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

Step-by-step 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 $y' = \frac{2\cdot x}{\sqrt{x^{2}+2\cdot x +2}}$.