Calculus Examples

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

Step 1

Simplify with factoring out.

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Step 1.1

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

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

Step 1.2

Simplify the expression.

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Step 1.2.1

Apply the product rule to $3 (x^{2})$ .

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

Step 1.2.2

Raise $3$ to the power of $2$ .

$\frac{d}{d x} [9 {(x^{2})}^{2}]$

Step 1.2.3

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 1.2.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{d}{d x} [9 x^{2 \cdot 2}]$

Step 1.2.3.2

Multiply $2$ by $2$ .

$\frac{d}{d x} [9 x^{4}]$

Step 2

Since $9$ is constant with respect to $x$ , the derivative of $9 x^{4}$ with respect to $x$ is $9 \frac{d}{d x} [x^{4}]$ .

$9 \frac{d}{d x} [x^{4}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 4$ .

$9 (4 x^{3})$

Step 4

Multiply $4$ by $9$ .

$36 x^{3}$