Solve 1/2*x*x*x*(-2y)*(-y)*(-y)

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

Evaluate

$$-\left(xy\right)^{3}$$

Solution Steps

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

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

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

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

Multiply -y and -y to get \left(-y\right)^{2}.

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

Multiply \frac{1}{2} and -2 to get \frac{-2}{2}.

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

Divide -2 by 2 to get -1.

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

Calculate -y to the power of 2 and get y^{2}.

$$-x^{3}yy^{2}$$

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

$$-x^{3}y^{3}$$

Differentiate w.r.t. x

$$-3x^{2}y^{3}$$