Solve -3y(-6y^5)

$$- 3 y ( - 6 y ^ { 5 } )$$

Evaluate

$$18y^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$-3y^{6}\left(-6\right)$$

Multiply -3 and -6 to get 18.

$$18y^{6}$$

Differentiate w.r.t. y

$$108y^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-3y^{6}\left(-6\right))$$

Multiply -3 and -6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}y}(18y^{6})$$

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

$$6\times 18y^{6-1}$$

Multiply 6 times 18.

$$108y^{6-1}$$

Subtract 1 from 6.

$$108y^{5}$$