Solve (8y)(3y)(-2y)

$$( 8 y ) ( 3 y ) ( - 2 y )$$

Evaluate

$$-48y^{3}$$

Solution Steps

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

$$8y^{2}\times 3\left(-2\right)y$$

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

$$8y^{3}\times 3\left(-2\right)$$

Multiply 8 and 3 to get 24.

$$24y^{3}\left(-2\right)$$

Multiply 24 and -2 to get -48.

$$-48y^{3}$$

Differentiate w.r.t. y

$$-144y^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(8y^{2}\times 3\left(-2\right)y)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(8y^{3}\times 3\left(-2\right))$$

Multiply 8 and 3 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}y}(24y^{3}\left(-2\right))$$

Multiply 24 and -2 to get -48.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-48y^{3})$$

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

$$3\left(-48\right)y^{3-1}$$

Multiply 3 times -48.

$$-144y^{3-1}$$

Subtract 1 from 3.

$$-144y^{2}$$