Solve d/dleft(xxxright)left(x*y*(2-x-y+1right)

$$\frac{d}{d \left(xxx \right) } \left(x \times y \times (2-x-y+1 \right)$$

Evaluate

$$\frac{y\left(3-y-x\right)}{x^{2}}$$

Short Solution Steps

Multiply x and x to get x^{2}.

$$\frac{d}{dx^{2}x}xy\left(2-x-y+1\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{d}{dx^{3}}xy\left(2-x-y+1\right)$$

Cancel out d in both numerator and denominator.

$$\frac{1}{x^{3}}xy\left(2-x-y+1\right)$$

Add 2 and 1 to get 3.

$$\frac{1}{x^{3}}xy\left(3-x-y\right)$$

Express \frac{1}{x^{3}}x as a single fraction.

$$\frac{x}{x^{3}}y\left(3-x-y\right)$$

Cancel out x in both numerator and denominator.

$$\frac{1}{x^{2}}y\left(3-x-y\right)$$

Express \frac{1}{x^{2}}y as a single fraction.

$$\frac{y}{x^{2}}\left(3-x-y\right)$$

Express \frac{y}{x^{2}}\left(3-x-y\right) as a single fraction.

$$\frac{y\left(3-x-y\right)}{x^{2}}$$

Use the distributive property to multiply y by 3-x-y.

$$\frac{3y-yx-y^{2}}{x^{2}}$$

Expand

$$\frac{3y-y^{2}-xy}{x^{2}}$$

Short Solution Steps

Multiply x and x to get x^{2}.

$$\frac{d}{dx^{2}x}xy\left(2-x-y+1\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{d}{dx^{3}}xy\left(2-x-y+1\right)$$

Cancel out d in both numerator and denominator.

$$\frac{1}{x^{3}}xy\left(2-x-y+1\right)$$

Add 2 and 1 to get 3.

$$\frac{1}{x^{3}}xy\left(3-x-y\right)$$

Express \frac{1}{x^{3}}x as a single fraction.

$$\frac{x}{x^{3}}y\left(3-x-y\right)$$

Cancel out x in both numerator and denominator.

$$\frac{1}{x^{2}}y\left(3-x-y\right)$$

Express \frac{1}{x^{2}}y as a single fraction.

$$\frac{y}{x^{2}}\left(3-x-y\right)$$

Express \frac{y}{x^{2}}\left(3-x-y\right) as a single fraction.

$$\frac{y\left(3-x-y\right)}{x^{2}}$$

Use the distributive property to multiply y by 3-x-y.

$$\frac{3y-yx-y^{2}}{x^{2}}$$