Solve (11x^3)(2x^4)

$$( 11 x ^ { 3 } ) ( 2 x ^ { 4 } )$$

Evaluate

$$22x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$11x^{7}\times 2$$

Multiply 11 and 2 to get 22.

$$22x^{7}$$

Differentiate w.r.t. x

$$154x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{7}\times 2)$$

Multiply 11 and 2 to get 22.

$$\frac{\mathrm{d}}{\mathrm{d}x}(22x^{7})$$

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

$$7\times 22x^{7-1}$$

Multiply 7 times 22.

$$154x^{7-1}$$

Subtract 1 from 7.

$$154x^{6}$$