Solve -2y^6(-8y)

$$- 2 y ^ { 6 } ( - 8 y )$$

Evaluate

$$16y^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-2y^{7}\left(-8\right)$$

Multiply -2 and -8 to get 16.

$$16y^{7}$$

Differentiate w.r.t. y

$$112y^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-2y^{7}\left(-8\right))$$

Multiply -2 and -8 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(16y^{7})$$

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

$$7\times 16y^{7-1}$$

Multiply 7 times 16.

$$112y^{7-1}$$

Subtract 1 from 7.

$$112y^{6}$$