Solve (9x^6)(2x^5)

$$( 9 x ^ { 6 } ) ( 2 x ^ { 5 } )$$

Evaluate

$$18x^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$9x^{11}\times 2$$

Multiply 9 and 2 to get 18.

$$18x^{11}$$

Differentiate w.r.t. x

$$198x^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{11}\times 2)$$

Multiply 9 and 2 to get 18.

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

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

$$11\times 18x^{11-1}$$

Multiply 11 times 18.

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

Subtract 1 from 11.

$$198x^{10}$$