Calculus Examples

$2 x^{3} y$

Step 1

Since $2 y$ is constant with respect to $x$ , the derivative of $2 x^{3} y$ with respect to $x$ is $2 y \frac{d}{d x} [x^{3}]$ .

$2 y \frac{d}{d x} [x^{3}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$2 y (3 x^{2})$

Step 3

Simplify the expression.

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Step 3.1

Multiply $3$ by $2$ .

$6 y x^{2}$

Step 3.2

Reorder the factors of $6 y x^{2}$ .

$6 x^{2} y$