Originally Posted by

**looi76** **Question:**

Differentiate $\displaystyle \sqrt{(x^2 + 1)}$ with respect to $\displaystyle x$.

**Attempt:**

$\displaystyle \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$

$\displaystyle u = \sqrt{(x^2 + 1)} = (x^2 + 1)^{\frac{1}{2}}$

$\displaystyle \frac{dy}{du} = x^2$

$\displaystyle \frac{du}{dx} = \frac{1}{2}u^{-\frac{1}{2}}$

$\displaystyle \frac{dy}{dx} = x^2 \times \frac{1}{2}u^{-\frac{1}{2}}$

$\displaystyle \frac{dy}{dx} = x^2 \times \frac{1}{2}(x^2 + 1)^{-\frac{1}{2}}$

Are my steps right? and can you please complete the steps? thnx!