Calculus Examples

$\frac{4 x^{3}}{3 y^{2}}$

Step 1

Since $\frac{4}{3 y^{2}}$ is constant with respect to $x$ , the derivative of $\frac{4 x^{3}}{3 y^{2}}$ with respect to $x$ is $\frac{4}{3 y^{2}} \frac{d}{d x} [x^{3}]$ .

$\frac{4}{3 y^{2}} \frac{d}{d x} [x^{3}]$

Step 2

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

$\frac{4}{3 y^{2}} (3 x^{2})$

Step 3

Simplify terms.

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Step 3.1

Combine $3$ and $\frac{4}{3 y^{2}}$ .

$\frac{3 \cdot 4}{3 y^{2}} x^{2}$

Step 3.2

Multiply $3$ by $4$ .

$\frac{12}{3 y^{2}} x^{2}$

Step 3.3

Combine $\frac{12}{3 y^{2}}$ and $x^{2}$ .

$\frac{12 x^{2}}{3 y^{2}}$

Step 3.4

Cancel the common factor of $12$ and $3$ .

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Step 3.4.1

Factor $3$ out of $12 x^{2}$ .

$\frac{3 (4 x^{2})}{3 y^{2}}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

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

$\frac{3 (4 x^{2})}{3 (y^{2})}$

Step 3.4.2.2

Cancel the common factor.

$\frac{3 (4 x^{2})}{3 y^{2}}$

Step 3.4.2.3

Rewrite the expression.

$\frac{4 x^{2}}{y^{2}}$