Calculus Examples

$24 x^{3} y^{2}$

Step 1

Since $24 y^{2}$ is constant with respect to $x$ , the derivative of $24 x^{3} y^{2}$ with respect to $x$ is $24 y^{2} \frac{d}{d x} [x^{3}]$ .

$24 y^{2} \frac{d}{d x} [x^{3}]$

Step 2

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

$24 y^{2} (3 x^{2})$

Step 3

Simplify the expression.

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Step 3.1

Multiply $3$ by $24$ .

$72 y^{2} x^{2}$

Step 3.2

Reorder the factors of $72 y^{2} x^{2}$ .

$72 x^{2} y^{2}$