Solve (-2y^4)(8y^2)

$$( - 2 y ^ { 4 } ) ( 8 y ^ { 2 } )$$

Evaluate

$$-16y^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-2y^{6}\times 8$$

Multiply -2 and 8 to get -16.

$$-16y^{6}$$

Differentiate w.r.t. y

$$-96y^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-2y^{6}\times 8)$$

Multiply -2 and 8 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-16y^{6})$$

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

$$6\left(-16\right)y^{6-1}$$

Multiply 6 times -16.

$$-96y^{6-1}$$

Subtract 1 from 6.

$$-96y^{5}$$