Solve (2y^8)(9y^9)=

$$( 2 y ^ { 8 } ) ( 9 y ^ { 9 } ) =$$

Evaluate

$$18y^{17}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$2y^{17}\times 9$$

Multiply 2 and 9 to get 18.

$$18y^{17}$$

Differentiate w.r.t. y

$$306y^{16}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{17}\times 9)$$

Multiply 2 and 9 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}y}(18y^{17})$$

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

$$17\times 18y^{17-1}$$

Multiply 17 times 18.

$$306y^{17-1}$$

Subtract 1 from 17.

$$306y^{16}$$