Calculus Examples

$(4 - x) y^{2}$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

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

$(4 - x) \frac{d}{d y} [y^{2}]$

Step 3

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

$(4 - x) (2 y)$

Step 4

Move $2$ to the left of $4 - x$ .

$2 \cdot (4 - x) y$

Step 5

Simplify.

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Step 5.1

Apply the distributive property.

$(2 \cdot 4 + 2 (- x)) y$

Step 5.2

Apply the distributive property.

$2 \cdot 4 y + 2 (- x) y$

Step 5.3

Combine terms.

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Step 5.3.1

Multiply $2$ by $4$ .

$8 y + 2 (- x) y$

Step 5.3.2

Multiply $- 1$ by $2$ .

$8 y - 2 x y$

Step 5.4

Reorder terms.

$- 2 x y + 8 y$