Question

differentiate.
$h(u)=(u - \sqrt{u})(u + \sqrt{u})$
$h(u)=$

Explanation:

Step1: Simplify the function

Use the difference - of - squares formula $(a - b)(a + b)=a^{2}-b^{2}$. Here $a = u$ and $b=\sqrt{u}$, so $H(u)=u^{2}-u$.

Step2: Differentiate term - by - term

The derivative of $u^{n}$ with respect to $u$ is $nu^{n - 1}$. For $y = u^{2}$, $y^\prime=2u$, and for $y = u$, $y^\prime = 1$. So $H^\prime(u)=\frac{d}{du}(u^{2}-u)=\frac{d}{du}(u^{2})-\frac{d}{du}(u)$.

Step3: Calculate the derivative

$H^\prime(u)=2u - 1$.

Answer:

$2u - 1$