Calculus Examples

$y = \sqrt{x^{2} + 3 x}$

Step 1

Factor $x$ out of $x^{2} + 3 x$ .

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Step 1.1

Factor $x$ out of $x^{2}$ .

$\frac{d}{d y} [\sqrt{x \cdot x + 3 x}]$

Step 1.2

Factor $x$ out of $3 x$ .

$\frac{d}{d y} [\sqrt{x \cdot x + x \cdot 3}]$

Step 1.3

Factor $x$ out of $x \cdot x + x \cdot 3$ .

$\frac{d}{d y} [\sqrt{x (x + 3)}]$

Step 2

Since $\sqrt{x (x + 3)}$ is constant with respect to $y$ , the derivative of $\sqrt{x (x + 3)}$ with respect to $y$ is $0$ .

$0$