Solve (3x^7)(11x^6)

$$( 3 x ^ { 7 } ) ( 11 x ^ { 6 } )$$

Evaluate

$$33x^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$3x^{13}\times 11$$

Multiply 3 and 11 to get 33.

$$33x^{13}$$

Differentiate w.r.t. x

$$429x^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{13}\times 11)$$

Multiply 3 and 11 to get 33.

$$\frac{\mathrm{d}}{\mathrm{d}x}(33x^{13})$$

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

$$13\times 33x^{13-1}$$

Multiply 13 times 33.

$$429x^{13-1}$$

Subtract 1 from 13.

$$429x^{12}$$