Calculus Examples

$\frac{5 x^{4}}{3 y^{2}}$

Step 1

Since $\frac{5}{3 y^{2}}$ is constant with respect to $x$ , the derivative of $\frac{5 x^{4}}{3 y^{2}}$ with respect to $x$ is $\frac{5}{3 y^{2}} \frac{d}{d x} [x^{4}]$ .

$\frac{5}{3 y^{2}} \frac{d}{d x} [x^{4}]$

Step 2

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

$\frac{5}{3 y^{2}} (4 x^{3})$

Step 3

Combine fractions.

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Step 3.1

Combine $4$ and $\frac{5}{3 y^{2}}$ .

$\frac{4 \cdot 5}{3 y^{2}} x^{3}$

Step 3.2

Multiply $4$ by $5$ .

$\frac{20}{3 y^{2}} x^{3}$

Step 3.3

Combine $\frac{20}{3 y^{2}}$ and $x^{3}$ .

$\frac{20 x^{3}}{3 y^{2}}$