Calculus Examples

$- \frac{6 x^{2}}{2 y - 1}$

Step 1

Since $- \frac{6}{2 y - 1}$ is constant with respect to $x$ , the derivative of $- \frac{6 x^{2}}{2 y - 1}$ with respect to $x$ is $- \frac{6}{2 y - 1} \frac{d}{d x} [x^{2}]$ .

$- \frac{6}{2 y - 1} \frac{d}{d x} [x^{2}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$- \frac{6}{2 y - 1} (2 x)$

Step 3

Combine fractions.

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Step 3.1

Multiply $2$ by $- 1$ .

$- 2 \frac{6}{2 y - 1} x$

Step 3.2

Combine $- 2$ and $\frac{6}{2 y - 1}$ .

$\frac{- 2 \cdot 6}{2 y - 1} x$

Step 3.3

Multiply $- 2$ by $6$ .

$\frac{- 12}{2 y - 1} x$

Step 3.4

Combine $\frac{- 12}{2 y - 1}$ and $x$ .

$\frac{- 12 x}{2 y - 1}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{12 x}{2 y - 1}$