Calculus Examples

$y^{2} (6 - 2 x)$

Step 1

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

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

Step 2

By the Sum Rule, the derivative of $6 - 2 x$ with respect to $x$ is $\frac{d}{d x} [6] + \frac{d}{d x} [- 2 x]$ .

$y^{2} (\frac{d}{d x} [6] + \frac{d}{d x} [- 2 x])$

Step 3

Since $6$ is constant with respect to $x$ , the derivative of $6$ with respect to $x$ is $0$ .

$y^{2} (0 + \frac{d}{d x} [- 2 x])$

Step 4

Add $0$ and $\frac{d}{d x} [- 2 x]$ .

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

Step 5

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

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

Step 6

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

$y^{2} (- 2 \cdot 1)$

Step 7

Simplify the expression.

Tap for more steps...

Step 7.1

Multiply $- 2$ by $1$ .

$y^{2} \cdot - 2$

Step 7.2

Move $- 2$ to the left of $y^{2}$ .

$- 2 y^{2}$