Solve (-y)*(-y)*(-y)

$$( - y ) \times ( - y ) \times ( - y )$$

Evaluate

$$-y^{3}$$

Solution Steps

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

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

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

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

Expand \left(-y\right)^{3}.

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

Calculate -1 to the power of 3 and get -1.

$$-y^{3}$$

Differentiate w.r.t. y

$$-3y^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-y\right)^{2}\left(-y\right))$$

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

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

Expand \left(-y\right)^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-1\right)^{3}y^{3})$$

Calculate -1 to the power of 3 and get -1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-y^{3})$$

The derivative of ax^{n} is nax^{n-1}.

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

Multiply 3 times -1.

$$-3y^{3-1}$$

Subtract 1 from 3.

$$-3y^{2}$$