Calculus Examples

$x^{2} y$

Step 1

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

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

Step 2

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

$y (2 x)$

Step 3

Reorder.

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Step 3.1

Move $2$ to the left of $y$ .

$2 \cdot y x$

Step 3.2

Reorder the factors of $2 y x$ .

$2 x y$