Calculus Examples

${(x y)}^{2}$

Step 1

Apply the product rule to $x y$ .

$\frac{d}{d x} [x^{2} y^{2}]$

Step 2

Since $y^{2}$ is constant with respect to $x$ , the derivative of $x^{2} y^{2}$ with respect to $x$ is $y^{2} \frac{d}{d x} [x^{2}]$ .

$y^{2} \frac{d}{d x} [x^{2}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$y^{2} (2 x)$

Step 4

Move $2$ to the left of $y^{2}$ .

$2 y^{2} x$