Calculus Examples

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

Step 1

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

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

Step 2

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

$(6 - 2 x) (2 y)$

Step 3

Move $2$ to the left of $6 - 2 x$ .

$2 \cdot (6 - 2 x) y$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$(2 \cdot 6 + 2 (- 2 x)) y$

Step 4.2

Apply the distributive property.

$2 \cdot 6 y + 2 (- 2 x) y$

Step 4.3

Combine terms.

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Step 4.3.1

Multiply $2$ by $6$ .

$12 y + 2 (- 2 x) y$

Step 4.3.2

Multiply $- 2$ by $2$ .

$12 y - 4 x y$

Step 4.4

Reorder terms.

$- 4 x y + 12 y$