Solve (6y^7)(-3y^4)

$$( 6 y ^ { 7 } ) ( - 3 y ^ { 4 } )$$

Evaluate

$$-18y^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$6y^{11}\left(-3\right)$$

Multiply 6 and -3 to get -18.

$$-18y^{11}$$

Differentiate w.r.t. y

$$-198y^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{11}\left(-3\right))$$

Multiply 6 and -3 to get -18.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-18y^{11})$$

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

$$11\left(-18\right)y^{11-1}$$

Multiply 11 times -18.

$$-198y^{11-1}$$

Subtract 1 from 11.

$$-198y^{10}$$